JEE Main & Advanced Mathematics Differential Equations Question Bank

done Linear defferential equations Total Questions - 39

• question_answer1)
  Which of the following equation is non-linear
  A)
                  \[\frac{dy}{dx}+\frac{y}{x}=\log x\] done clear
  B)
                  \[y\frac{dy}{dx}+4x=0\] done clear
  C)
                  \[dx+dy=0\]          done clear
  D)
                  \[\frac{dy}{dx}=\cos x\] done clear
  View Solution play_arrow

• question_answer2)
  Which of the following equation is linear
  A)
                  \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{^{2}}}+{{x}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}=0\]       done clear
  B)
                  \[y=\frac{dy}{dx}+\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}\] done clear
  C)
                  \[\frac{dy}{dx}+\frac{y}{x}=\log x\] done clear
  D)
                  \[y\frac{dy}{dx}-4=x\] done clear
  View Solution play_arrow

• question_answer3)
  The solution of the equation \[\frac{dy}{dx}+y\tan x={{x}^{m}}\cos x\] is
  A)
                  \[(m+1)y={{x}^{m+1}}\cos x+c(m+1)\cos x\] done clear
  B)
                  \[my=({{x}^{m}}+c)\cos x\] done clear
  C)
                  \[y=({{x}^{m+1}}+c)\cos x\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer4)
  An integrating factor for the differential equation \[(1+{{y}^{2}})dx-({{\tan }^{-1}}y-x)dy=0\]         [MP PET 1993]
  A)
                  \[{{\tan }^{-1}}y\]              done clear
  B)
                  \[{{e}^{{{\tan }^{-1}}y}}\] done clear
  C)
                  \[\frac{1}{1+{{y}^{2}}}\]                done clear
  D)
                  \[\frac{1}{x(1+{{y}^{2}})}\] done clear
  View Solution play_arrow

• question_answer5)
  The equation of the curve passing through the origin and satisfying the equation \[(1+{{x}^{2}})\frac{dy}{dx}+2xy=4{{x}^{2}}\] is               
  A)
                  \[3(1+{{x}^{2}})y=4{{x}^{3}}\] done clear
  B)
                  \[3(1-{{x}^{2}})y=4{{x}^{3}}\] done clear
  C)
                  \[3(1+{{x}^{2}})={{x}^{3}}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer6)
  Which of the following equation is non-linear
  A)
                  \[\frac{dy}{dx}=\cos x\]       done clear
  B)
                  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\] done clear
  C)
                  \[dx+dy=0\]          done clear
  D)
                  \[x\frac{dy}{dx}+\frac{3}{\frac{dy}{dx}}={{y}^{2}}\] done clear
  View Solution play_arrow

• question_answer7)
  The solution of the differential equation \[\frac{dy}{dx}+\frac{y}{x}={{x}^{2}}\]is
  A)
                  \[4xy={{x}^{4}}+c\]        done clear
  B)
                  \[xy={{x}^{4}}+c\] done clear
  C)
                  \[\frac{1}{4}xy={{x}^{4}}+c\]       done clear
  D)
                  \[xy=4{{x}^{4}}+c\] done clear
  View Solution play_arrow

• question_answer8)
  The solution of the differential equation \[x\frac{dy}{dx}+y={{x}^{2}}+3x+2\] is
  A)
                  \[xy=\frac{{{x}^{3}}}{3}+\frac{3}{2}{{x}^{2}}+2x+c\]      done clear
  B)
                  \[xy=\frac{{{x}^{4}}}{4}+{{x}^{3}}+{{x}^{2}}+c\] done clear
  C)
                  \[xy=\frac{{{x}^{4}}}{4}+\frac{{{x}^{3}}}{3}+{{x}^{2}}+c\]         done clear
  D)
                  \[xy=\frac{{{x}^{4}}}{4}+{{x}^{3}}+{{x}^{2}}+cx\] done clear
  View Solution play_arrow

• question_answer9)
  The solution of the differential equation \[\frac{dy}{dx}+\frac{3{{x}^{2}}}{1+{{x}^{3}}}y=\frac{{{\sin }^{2}}x}{1+{{x}^{3}}}\] is
  A)
                  \[y(1+{{x}^{3}})=x+\frac{1}{2}\sin 2x+c\] done clear
  B)
                  \[y(1+{{x}^{3}})=cx+\frac{1}{2}\sin 2x\] done clear
  C)
                  \[y(1+{{x}^{3}})=cx-\frac{1}{2}\sin 2x\] done clear
  D)
                  \[y(1+{{x}^{3}})=\frac{x}{2}-\frac{1}{4}\sin 2x+c\] done clear
  View Solution play_arrow

• question_answer10)
  Which of the following equation is linear
  A)
                  \[\frac{dy}{dx}+x{{y}^{2}}=1\]    done clear
  B)
                  \[{{x}^{2}}\frac{dy}{dx}+y={{e}^{x}}\] done clear
  C)
                  \[\frac{dy}{dx}+3y=x{{y}^{2}}\]  done clear
  D)
                  \[x\frac{dy}{dx}+{{y}^{2}}=\sin x\] done clear
  View Solution play_arrow

• question_answer11)
  The solution of the equation \[x\frac{dy}{dx}+3y=x\] is
  A)
                  \[{{x}^{3}}y+\frac{{{x}^{4}}}{4}+c=0\] done clear
  B)
                  \[{{x}^{3}}y=\frac{{{x}^{4}}}{4}+c\] done clear
  C)
                  \[{{x}^{3}}y+\frac{{{x}^{4}}}{4}=0\]      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer12)
  The solution of the differential equation \[\frac{dy}{dx}+y=\cos x\]is [AISSE 1990]
  A)
                  \[y=\frac{1}{2}(\cos x+\sin x)+c{{e}^{-x}}\]               done clear
  B)
                  \[y=\frac{1}{2}(\cos x-\sin x)+c{{e}^{-x}}\] done clear
  C)
                  \[y=\cos x+\sin x+c{{e}^{-x}}\]      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer13)
  The solution of the differential equation \[\frac{dy}{dx}+y\cot x=2\cos x\] is
  A)
                  \[y\sin x+\cos 2x=2c\]          done clear
  B)
                  \[2y\sin x+\cos x=c\] done clear
  C)
                  \[y\sin x+\cos x=c\]              done clear
  D)
                  \[2y\sin x+\cos 2x=c\] done clear
  View Solution play_arrow

• question_answer14)
  The solution of the equation \[(x+2{{y}^{3}})\frac{dy}{dx}-y=0\] is [MP PET 1998; 2002]
  A)
                  \[y(1-xy)=Ax\]       done clear
  B)
                  \[{{y}^{3}}-x=Ay\] done clear
  C)
                  \[x(1-xy)=Ay\]       done clear
  D)
                  \[x(1+xy)=Ay\] Where A is any arbitrary constant done clear
  View Solution play_arrow

• question_answer15)
  The integrating factor of the differential equation \[\frac{dy}{dx}=y\tan x-{{y}^{2}}\sec x,\]is               [MP PET 1995; Pb. CET 2002]
  A)
                  \[\tan x\]  done clear
  B)
                  \[\sec x\] done clear
  C)
                  \[-\sec x\] done clear
  D)
                  \[\cot x\] done clear
  View Solution play_arrow

• question_answer16)
  Integrating factor of differential equation \[\cos x\frac{dy}{dx}+y\sin x=1\]is              [MP PET 1996]
  A)
                  \[\cos x\]  done clear
  B)
                  \[\tan x\] done clear
  C)
                  \[\sec x\]  done clear
  D)
                  \[\sin x\] done clear
  View Solution play_arrow

• question_answer17)
  Solution of differential equation \[\frac{dy}{dx}+ay={{e}^{mx}}\] is [MP PET 1996]
  A)
                  \[(a+m)\,y={{e}^{mx}}+c\]            done clear
  B)
                  \[y{{e}^{ax}}=m{{e}^{mx}}+c\] done clear
  C)
                  \[y={{e}^{mx}}+c{{e}^{-ax}}\] done clear
  D)
                  \[(a+m)y={{e}^{mx}}+c{{e}^{-ax}}(a+m)\] done clear
  View Solution play_arrow

• question_answer18)
  The integrating factor of the differential equation \[(x\log x)\frac{dy}{dx}+y=2\log x\] is
  A)
                  \[\log x\]  done clear
  B)
                  \[\log (\log x)\] done clear
  C)
                  \[{{e}^{x}}\]       done clear
  D)
                  \[x\] done clear
  View Solution play_arrow

• question_answer19)
  Integrating factor of the differential equation \[\frac{dy}{dx}+y\tan x-\sec x=0\] is      [MP PET 2002]
  A)
                  \[{{e}^{\sin x}}\] done clear
  B)
                  \[\frac{1}{\sin x}\] done clear
  C)
                  \[\frac{1}{\cos x}\] done clear
  D)
                  \[{{e}^{\cos x}}\] done clear
  View Solution play_arrow

• question_answer20)
  The solution of the differential equation \[x\log x\frac{dy}{dx}+y=2\log x\] is
  A)
                  \[y=\log x+c\]        done clear
  B)
                  \[y=\log {{x}^{2}}+c\] done clear
  C)
                  \[y\log x={{(\log x)}^{2}}+c\]         done clear
  D)
                  \[y=x\log x+c\] done clear
  View Solution play_arrow

• question_answer21)
  The solution of the differential equation \[\frac{dy}{dx}+2y\cot x=3{{x}^{2}}\text{cose}{{\text{c}}^{2}}x\]is
  A)
                  \[y{{\sin }^{2}}x={{x}^{3}}+c\] done clear
  B)
                  \[y\sin x=c\] done clear
  C)
                  \[y\cos {{x}^{2}}=c\]        done clear
  D)
                  \[y\sin {{x}^{2}}=c\] done clear
  View Solution play_arrow

• question_answer22)
  Solution of differential equation \[x\frac{dy}{dx}=y+{{x}^{^{2}}}\] is [MP PET 1997]
  A)
                  \[y={{\log }_{e}}x+\frac{{{x}^{2}}}{2}+a\]              done clear
  B)
                  \[y=\frac{{{x}^{3}}}{3}+\frac{a}{x}\] done clear
  C)
                  \[y={{x}^{2}}+ax\]          done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer23)
  Integrating factor of \[\frac{dy}{dx}+\frac{y}{x}={{x}^{3}}-3\]is              [MP PET 1999]
  A)
                  \[x\]         done clear
  B)
                  \[\log x\] done clear
  C)
                  \[-x\]        done clear
  D)
                  \[{{e}^{x}}\] done clear
  View Solution play_arrow

• question_answer24)
  Solution of \[\cos x\frac{dy}{dx}+y\sin x=1\]is               [MP PET 1999]
  A)
                  \[y\sec x\tan x=c\]  done clear
  B)
                  \[y\sec x\tan x=c\] done clear
  C)
                  \[y\tan x=\sec x+c\]              done clear
  D)
                  \[y\tan x=\sec x\tan x+c\] done clear
  View Solution play_arrow

• question_answer25)
  The solution of \[\frac{dy}{dx}+2y\,\tan x=\sin x\], is     [DCE 1999]
  A)
                  \[y\,{{\sec }^{3}}x={{\sec }^{2}}x+c\]        done clear
  B)
                  \[y\,{{\sec }^{2}}x=\sec x+c\] done clear
  C)
                  \[y\,\,\sin x=\tan x+c\]           done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer26)
  Solution of the differential equation \[\frac{dy}{dx}+y{{\sec }^{2}}x=\tan x{{\sec }^{2}}x\] is         [DCE 2001, 05]
  A)
                  \[y=\tan x-1+c{{e}^{-\tan x}}\] done clear
  B)
                  \[{{y}^{2}}=\tan x-1+c{{e}^{\tan x}}\] done clear
  C)
                  \[y{{e}^{\tan x}}=\tan x-1+c\]         done clear
  D)
                  \[y{{e}^{-\tan x}}=\tan x-1+c\] done clear
  View Solution play_arrow

• question_answer27)
  An integrating factor of the differential equation \[(1-{{x}^{2}})\frac{dy}{dx}-xy=1,\] is        [MP PET 2001]
  A)
                  ? x           done clear
  B)
                  \[-\frac{x}{(1-{{x}^{2}})}\] done clear
  C)
                  \[\sqrt{(1-{{x}^{2}})}\]     done clear
  D)
                  \[\frac{1}{2}\log (1-{{x}^{2}})\] done clear
  View Solution play_arrow

• question_answer28)
  Integrating factor of equation \[({{x}^{2}}+1)\frac{dy}{dx}+2xy={{x}^{2}}-1\] is [UPSEAT 2002]
  A)
                  \[{{x}^{2}}+1\] done clear
  B)
                  \[\frac{2x}{{{x}^{2}}+1}\] done clear
  C)
                  \[\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\]          done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer29)
  The solution of \[\frac{dy}{dx}+\frac{y}{3}=1\] is         [EAMCET 2002]
  A)
                  \[y=3+c{{e}^{x/3}}\]       done clear
  B)
                  \[y=3+c{{e}^{-x/3}}\] done clear
  C)
                  \[3y=c+{{e}^{x/3}}\]       done clear
  D)
                  \[3y=c+{{e}^{-x/3}}\] done clear
  View Solution play_arrow

• question_answer30)
  \[y+{{x}^{2}}=\frac{dy}{dx}\] has the solution          [EAMCET 2002]
  A)
                  \[y+{{x}^{2}}+2x+2=c{{e}^{x}}\]           done clear
  B)
                  \[y+x+{{x}^{2}}+2=c{{e}^{2x}}\] done clear
  C)
                  \[y+x+2{{x}^{2}}+2=c{{e}^{x}}\]           done clear
  D)
                  \[{{y}^{2}}+x+{{x}^{2}}+2=c{{e}^{x}}\] done clear
  View Solution play_arrow

• question_answer31)
  The solution of \[\frac{dy}{dx}+p(x)y=0\] is   [Kerala (Engg.)  2002]
  A)
                  \[y=c{{e}^{\int{p\,d\,x}}}\]              done clear
  B)
                  \[x=c{{e}^{-\int{p\,d\,y}}}\] done clear
  C)
                  \[y=c{{e}^{-\int{P\,d\,x}}}\]             done clear
  D)
                  \[x=c{{e}^{\int{p\,d\,y}}}\] done clear
  View Solution play_arrow

• question_answer32)
  The solution of \[\frac{dy}{dx}+y={{e}^{-x}},\,\,y(0)=0\], is [Kerala (Engg.) 2002]
  A)
                  \[y={{e}^{-x}}(x-1)\]        done clear
  B)
                  \[y=x{{e}^{x}}\] done clear
  C)
                  \[y=x{{e}^{-x}}+1\]         done clear
  D)
                  \[y=x{{e}^{-x}}\] done clear
  View Solution play_arrow

• question_answer33)
  Integrating factor of the differential equation \[\frac{dy}{dx}+P(x)y=Q(x)\] is             [UPSEAT 2004]
  A)
                  \[\int{P\,dx}\]         done clear
  B)
                  \[\int{Q\,dx}\] done clear
  C)
                  \[{{e}^{\int{P\,dx}}}\]       done clear
  D)
                  \[{{e}^{\int{Q\,dx}}}\] done clear
  View Solution play_arrow

• question_answer34)
  To reduce the differential equation \[\frac{dy}{dx}+P(x)y=Q(x).{{y}^{n}}\] to the linear form, the substitution is             [UPSEAT 2004]
  A)
                  \[v=\frac{1}{{{y}^{n}}}\] done clear
  B)
                  \[v=\frac{1}{{{y}^{n-1}}}\] done clear
  C)
                  \[v={{y}^{n}}\]  done clear
  D)
                  \[v={{y}^{n-1}}\] done clear
  View Solution play_arrow

• question_answer35)
  The solution of differential equation \[\frac{dy}{dx}+y=1\] is [Pb. CET 2000]
  A)
                  \[y=1+c\,{{e}^{-x}}\]       done clear
  B)
                  \[y=1-c\,{{e}^{-x}}\] done clear
  C)
                  \[y=x+c\,{{e}^{-x}}\]        done clear
  D)
                  \[y=x-c\,{{e}^{-x}}\] done clear
  View Solution play_arrow

• question_answer36)
  The solution of \[dy=\cos x(2-y\cos \text{ec}x)dx\] where \[y=2\] when \[x=\frac{\pi }{2}\] is [J & K 2005]
  A)
                  \[y=\sin x+\text{cosec }x\]  done clear
  B)
                  \[y=\tan \frac{x}{2}+\cot \frac{x}{2}\] done clear
  C)
                  \[y=\frac{1}{\sqrt{2}}\sec \frac{x}{2}+\sqrt{2}\cos \frac{x}{2}\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer37)
  An integrating factor of the differential equation \[x\frac{dy}{dx}+y\log x=x{{e}^{x}}{{x}^{-\frac{1}{2}\log x}}\], \[(x>0)\] is [Kerala (Engg.) 2005]
  A)
                  \[{{x}^{\log x}}\]                done clear
  B)
                  \[{{(\sqrt{x})}^{\log x}}\] done clear
  C)
                  \[{{(\sqrt{e})}^{\log x}}\]  done clear
  D)
                  \[{{e}^{{{x}^{2}}}}\] done clear
  E)
                  \[{{x}^{2}}/2\] done clear
  View Solution play_arrow

• question_answer38)
  Solution of the differential equation \[\frac{dy}{dx}+\frac{y}{x}=\sin x\] is [Kerala (Engg.) 2005]
  A)
                  \[x(y+\cos x)=\sin x+c\]      done clear
  B)
                  \[x(y-\cos x)=\sin x+c\] done clear
  C)
                  \[x(y\cdot \cos x)=\sin x+c\] done clear
  D)
                  \[x(y-\cos x)=\cos x+c\] done clear
  E)
                  \[x(y+\cos x)=\cos x+c\] done clear
  View Solution play_arrow

• question_answer39)
  Solution of the equation \[(x+\log y)dy+y\,dx=0\] is
  A)
                  \[xy+y\log y=c\]    done clear
  B)
                  \[xy+y\log y-y=c\] done clear
  C)
                  \[xy+\log y-x=c\]  done clear
  D)
                  None of these done clear
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