JEE Main & Advanced Mathematics Differential Equations Question Bank

done Homogeneous differential equations Total Questions - 14

• question_answer1)
  The solution of the differential equation \[{{x}^{2}}\frac{dy}{dx}={{x}^{2}}+xy+{{y}^{2}}\] is
  A)
                  \[{{\tan }^{-1}}\left( \frac{y}{x} \right)=\log x+c\]        done clear
  B)
                  \[{{\tan }^{-1}}\left( \frac{y}{x} \right)=-\log x+c\] done clear
  C)
                  \[{{\sin }^{-1}}\left( \frac{y}{x} \right)=\log x+c\]         done clear
  D)
                  \[{{\tan }^{-1}}\left( \frac{x}{y} \right)=\log x+c\] done clear
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• question_answer2)
  Solution of differential equation \[2xy\frac{dy}{dx}={{x}^{2}}+3{{y}^{2}}\] is [MP PET 1993]
  A)
                  \[{{x}^{3}}+{{y}^{2}}=p{{x}^{2}}\]     done clear
  B)
                  \[\frac{{{x}^{2}}}{2}+\frac{{{y}^{3}}}{x}={{y}^{2}}+p\] done clear
  C)
                  \[{{x}^{2}}+{{y}^{3}}=p{{x}^{2}}\]     done clear
  D)
                  \[{{x}^{2}}+{{y}^{2}}=p{{x}^{3}}\] done clear
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• question_answer3)
  The solution of the differential equation \[({{x}^{2}}+{{y}^{2}})dx=2xydy\] is  [MP PET 2003; Orissa JEE 2005]
  A)
                  \[x=c({{x}^{2}}+{{y}^{2}})\]      done clear
  B)
                  \[x=c({{x}^{2}}-{{y}^{2}})\] done clear
  C)
                  \[x+c({{x}^{2}}-{{y}^{2}})=0\]  done clear
  D)
                  None of these done clear
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• question_answer4)
  The solution of the equation \[\frac{dy}{dx}=\frac{x+y}{x-y}\]is                [AI CBSE 1990]
  A)
                  \[c{{({{x}^{2}}+{{y}^{2}})}^{1/2}}+{{e}^{{{\tan }^{-1}}(y/x)}}=0\] done clear
  B)
                  \[c{{({{x}^{2}}+{{y}^{2}})}^{1/2}}={{e}^{{{\tan }^{-1}}(y/x)}}\] done clear
  C)
                  \[c({{x}^{2}}-{{y}^{2}})={{e}^{{{\tan }^{-1}}(y/x)}}\]     done clear
  D)
                  None of these done clear
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• question_answer5)
  The solution of the differential equation \[(3xy+{{y}^{2}})dx+({{x}^{2}}+xy)dy=0\] is [AISSE 1990]
  A)
                  \[{{x}^{2}}(2xy+{{y}^{2}})={{c}^{2}}\]               done clear
  B)
                  \[{{x}^{2}}(2xy-{{y}^{2}})={{c}^{2}}\] done clear
  C)
                  \[{{x}^{2}}({{y}^{2}}-2xy)={{c}^{2}}\] done clear
  D)
                  None of these done clear
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• question_answer6)
  The solution of the differential equation \[x\,dy-y\,dx=(\sqrt{{{x}^{2}}+{{y}^{2}})}dx\]is
  A)
                  \[y-\sqrt{{{x}^{2}}+{{y}^{2}}}=c{{x}^{2}}\]       done clear
  B)
                  \[y+\sqrt{{{x}^{2}}+{{y}^{2}}}=c{{x}^{2}}\] done clear
  C)
                  \[y+\sqrt{{{x}^{2}}+{{y}^{2}}}+c{{x}^{2}}=0\]                done clear
  D)
                  None of these done clear
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• question_answer7)
  The general solution of the differential equation \[(x+y)dx+xdy=0\] is        [MP PET 1994, 95]
  A)
                  \[{{x}^{2}}+{{y}^{2}}=c\]          done clear
  B)
                  \[2{{x}^{2}}-{{y}^{2}}=c\] done clear
  C)
                  \[{{x}^{2}}+2xy=c\]        done clear
  D)
                  \[{{y}^{2}}+2xy=c\] done clear
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• question_answer8)
  The solution of the differential equation \[x+y\frac{dy}{dx}=2y\] is
  A)
                  \[\log (y-x)=c+\frac{y-x}{x}\]             done clear
  B)
                  \[\log (y-x)=c+\frac{x}{y-x}\] done clear
  C)
                  \[y-x=c+\log \frac{x}{y-x}\]                done clear
  D)
                  \[y-x=c+\frac{x}{y-x}\] done clear
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• question_answer9)
  The solution of the differential equation \[\frac{dy}{dx}=\frac{xy}{{{x}^{2}}+{{y}^{2}}}\]is
  A)
                  \[a{{y}^{2}}={{e}^{{{x}^{2}}/{{y}^{2}}}}\]      done clear
  B)
                  \[ay={{e}^{x/y}}\] done clear
  C)
                  \[y={{e}^{{{x}^{2}}}}+{{e}^{{{y}^{2}}}}+c\] done clear
  D)
                  \[y={{e}^{{{x}^{2}}}}+{{y}^{2}}+c\] done clear
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• question_answer10)
  The solution of the equation \[\frac{dy}{dx}=\frac{x}{2y-x}\]is
  A)
                  \[(x-y){{(x+2y)}^{2}}=c\]                done clear
  B)
                  \[y=x+c\] done clear
  C)
                  \[y=(2y-x)+c\] done clear
  D)
                  \[y=\frac{x}{2y-x}+c\] done clear
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• question_answer11)
  The solution of the equation \[\frac{dy}{dx}=\frac{y}{x}\left( \log \frac{y}{x}+1 \right)\] is
  A)
                  \[\log \left( \frac{y}{x} \right)=cx\]       done clear
  B)
                  \[\frac{y}{x}=\log y+c\] done clear
  C)
                  \[y=\log y+1\]       done clear
  D)
                  \[y=xy+c\] done clear
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• question_answer12)
  Solution of differential equation \[\frac{dy}{dx}=\frac{y-x}{y+x}\]is [MP PET 1997]
  A)
                  \[{{\log }_{e}}({{x}^{2}}+{{y}^{2}})+2{{\tan }^{-1}}\frac{y}{x}+c=0\] done clear
  B)
                  \[\frac{{{y}^{2}}}{2}+xy=xy-\frac{{{x}^{2}}}{2}+c\] done clear
  C)
                  \[\left( 1+\frac{x}{y} \right)\text{ }y=\left( 1-\frac{x}{y} \right)\text{ }x+c\] done clear
  D)
                  \[y=x-2{{\log }_{e}}y+c\] done clear
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• question_answer13)
  If \[{y}'=\frac{x-y}{x+y}\], then its solution is                  [MP PET 2000]
  A)
                  \[{{y}^{2}}+2xy-{{x}^{2}}=c\]   done clear
  B)
                  \[{{y}^{2}}+2xy+{{x}^{2}}=c\] done clear
  C)
                  \[{{y}^{2}}-2xy-{{x}^{2}}=c\]     done clear
  D)
                  \[{{y}^{2}}-2xy+{{x}^{2}}=c\] done clear
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• question_answer14)
  The general solution of the differential equation \[(2x-y+1)dx+(2y-x+1)dy=0\] is    [Karnataka CET 2005]
  A)
                  \[{{x}^{2}}+{{y}^{2}}+xy-x+y=c\] done clear
  B)
              \[{{x}^{2}}+{{y}^{2}}-xy+x+y=c\] done clear
  C)
                  \[{{x}^{2}}-{{y}^{2}}+2xy-x+y=c\] done clear
  D)
                  \[{{x}^{2}}-{{y}^{2}}-2xy+x-y=c\] done clear
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