-
question_answer1)
\[y=4\sin 3x\]is a solution of the differential equation [AI CBSE 1986]
A)
\[\frac{dy}{dx}+8y=0\] done
clear
B)
\[\frac{dy}{dx}-8y=0\] done
clear
C)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+9y=0\] done
clear
D)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-9y=0\] done
clear
View Solution play_arrow
-
question_answer2)
The differential equation of all the lines in the xy-plane is
A)
\[\frac{dy}{dx}-x=0\] done
clear
B)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-x\frac{dy}{dx}=0\] done
clear
C)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\] done
clear
D)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+x=0\] done
clear
View Solution play_arrow
-
question_answer3)
The differential equation of the family of curves represented by the equation \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] is
A)
\[x+y\frac{dy}{dx}=0\] done
clear
B)
\[y\frac{dy}{dx}=x\] done
clear
C)
\[y\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer4)
\[y=\frac{x}{x+1}\] is a solution of the differential equation
A)
\[{{y}^{2}}\frac{dy}{dx}={{x}^{2}}\] done
clear
B)
\[{{x}^{2}}\frac{dy}{dx}={{y}^{2}}\] done
clear
C)
\[y\frac{dy}{dx}=x\] done
clear
D)
\[x\frac{dy}{dx}=y\] done
clear
View Solution play_arrow
-
question_answer5)
The differential equation whose solution is \[y=A\sin x+B\cos x,\] is [CEE 1993; Kerala (Engg.) 2002]
A)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\] done
clear
B)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-y=0\] done
clear
C)
\[\frac{dy}{dx}+y=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer6)
The differential equation of the family of curves \[y=a\cos (x+b)\] is [MP PET 1993]
A)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-y=0\] done
clear
B)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\] done
clear
C)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2y=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer7)
The differential equation for all the straight lines which are at a unit distance from the origin is [MP PET 1993]
A)
\[{{\left( y-x\frac{dy}{dx} \right)}^{2}}=1-{{\left( \frac{dy}{dx} \right)}^{2}}\] done
clear
B)
\[{{\left( y+x\frac{dy}{dx} \right)}^{2}}=1+{{\left( \frac{dy}{dx} \right)}^{2}}\] done
clear
C)
\[{{\left( y-x\frac{dy}{dx} \right)}^{2}}=1+{{\left( \frac{dy}{dx} \right)}^{2}}\] done
clear
D)
\[{{\left( y+x\frac{dy}{dx} \right)}^{2}}=1-{{\left( \frac{dy}{dx} \right)}^{2}}\] done
clear
View Solution play_arrow
-
question_answer8)
If \[y=c{{e}^{{{\sin }^{-1}}x}}\], then corresponding to this the differential equation is
A)
\[\frac{dy}{dx}=\frac{y}{\sqrt{1-{{x}^{2}}}}\] done
clear
B)
\[\frac{dy}{dx}=\frac{1}{\sqrt{1-{{x}^{2}}}}\]\[\] done
clear
C)
\[\frac{dy}{dx}=\frac{x}{\sqrt{1-{{x}^{2}}}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer9)
The differential equation of the family of curves represented by the equation \[{{x}^{2}}y=a\], is
A)
\[\frac{dy}{dx}+\frac{2y}{x}=0\] done
clear
B)
\[\frac{dy}{dx}+\frac{2x}{y}=0\] done
clear
C)
\[\frac{dy}{dx}-\frac{2y}{x}=0\] done
clear
D)
\[\frac{dy}{dx}-\frac{2x}{y}=0\] done
clear
View Solution play_arrow
-
question_answer10)
The differential equation corresponding to primitive \[y={{e}^{cx}}\]is or The elimination of the arbitrary constant m from the equation \[y={{e}^{mx}}\]gives the differential equation [MP PET 1995, 2000; Pb. CET 2000]
A)
\[\frac{dy}{dx}=\left( \frac{y}{x} \right)\log x\] done
clear
B)
\[\frac{dy}{dx}=\left( \frac{x}{y} \right)\log y\] done
clear
C)
\[\frac{dy}{dx}=\left( \frac{y}{x} \right)\log y\] done
clear
D)
\[\frac{dy}{dx}=\left( \frac{x}{y} \right)\log x\] done
clear
View Solution play_arrow
-
question_answer11)
The differential equation whose solution is \[y={{c}_{1}}\cos ax+{{c}_{2}}\sin ax\] is (Where \[{{c}_{1}},\ {{c}_{2}}\]are arbitrary constants) [MP PET 1996]
A)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{y}^{2}}=0\] done
clear
B)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{a}^{2}}y=0\] done
clear
C)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+a{{y}^{2}}=0\] done
clear
D)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{a}^{2}}y=0\] done
clear
View Solution play_arrow
-
question_answer12)
The differential equation for the line \[y=mx+c\] is (where c is arbitrary constant)
A)
\[\frac{dy}{dx}=m\] done
clear
B)
\[\frac{dy}{dx}+m=0\] done
clear
C)
\[\frac{dy}{dx}=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer13)
The differential equation of all straight lines passing through the point \[(1,\,-1)\]is [MP PET 1994]
A)
\[y=(x+1)\frac{dy}{dx}+1\] done
clear
B)
\[y=(x+1)\frac{dy}{dx}-1\] done
clear
C)
\[y=(x-1)\frac{dy}{dx}+1\] done
clear
D)
\[y=(x-1)\frac{dy}{dx}-1\] done
clear
View Solution play_arrow
-
question_answer14)
The differential equation of the family of curves \[{{y}^{2}}=4a(x+a)\], where a is an arbitrary constant, is
A)
\[y\text{ }\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\] done
clear
B)
\[y\text{ }\left[ 1-{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\] done
clear
C)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=0\] done
clear
D)
\[{{\left( \frac{dy}{dx} \right)}^{3}}+3\,\frac{dy}{dx}+y=0\] done
clear
View Solution play_arrow
-
question_answer15)
The differential equation of the family of curves \[v=\frac{A}{r}+B,\]where A and B are arbitrary constants, is
A)
\[\frac{{{d}^{2}}v}{d{{r}^{2}}}+\frac{1}{r}\frac{dv}{dr}=0\] done
clear
B)
\[\frac{{{d}^{2}}v}{d{{r}^{2}}}-\frac{2}{r}\frac{dv}{dr}=0\] done
clear
C)
\[\frac{{{d}^{2}}v}{d{{r}^{2}}}+\frac{2}{r}\frac{dv}{dr}=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer16)
The differential equation of all circles which passes through the origin and whose centre lies on y-axis, is [MNR 1986; DCE 2000]
A)
\[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}-2xy=0\] done
clear
B)
\[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}+2xy=0\] done
clear
C)
\[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}-xy=0\] done
clear
D)
\[({{x}^{2}}-{{y}^{2}})\frac{dy}{dx}+xy=0\] done
clear
View Solution play_arrow
-
question_answer17)
The differential equation of displacement of all "Simple harmonic motions" of given period \[2\pi /n\], is
A)
\[\frac{{{d}^{2}}x}{d{{t}^{2}}}+nx=0\] done
clear
B)
\[\frac{{{d}^{2}}x}{d{{t}^{2}}}+{{n}^{2}}x=0\] done
clear
C)
\[\frac{{{d}^{2}}x}{d{{t}^{2}}}-{{n}^{2}}x=0\] done
clear
D)
\[\frac{{{d}^{2}}x}{d{{t}^{2}}}+\frac{1}{{{n}^{2}}}x=0\] done
clear
View Solution play_arrow
-
question_answer18)
The differential equation of all parabolas whose axes are parallel to y-axis is
A)
\[\frac{{{d}^{3}}y}{d{{x}^{3}}}=0\] done
clear
B)
\[\frac{{{d}^{2}}x}{d{{y}^{2}}}=c\] done
clear
C)
\[\frac{{{d}^{3}}y}{d{{x}^{3}}}+\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\] done
clear
D)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=c\] done
clear
View Solution play_arrow
-
question_answer19)
The differential equation found by the elimination of the arbitrary constant K from the equation \[y=(x+K){{e}^{-x}}\]is
A)
\[\frac{dy}{dx}-y={{e}^{-x}}\] done
clear
B)
\[\frac{dy}{dx}-y{{e}^{x}}=1\] done
clear
C)
\[\frac{dy}{dx}+y{{e}^{x}}=1\] done
clear
D)
\[\frac{dy}{dx}+y={{e}^{-x}}\] done
clear
View Solution play_arrow
-
question_answer20)
Differential equation whose solution is \[y=cx+c-{{c}^{3}}\], is [MP PET 1997]
A)
\[\frac{dy}{dx}=c\] done
clear
B)
\[y=x\frac{dy}{dx}+\frac{dy}{dx}-{{\left( \frac{dy}{dx} \right)}^{3}}\] done
clear
C)
\[\frac{dy}{dx}=c-3{{c}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer21)
Family of curves \[y={{e}^{x}}(A\cos x+B\sin x)\], represents the differential equation [MP PET 1999]
A)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=2\frac{dy}{dx}-y\] done
clear
B)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=2\frac{dy}{dx}-2y\] done
clear
C)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{dy}{dx}-2y\] done
clear
D)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=2\frac{dy}{dx}+y\] done
clear
View Solution play_arrow
-
question_answer22)
The elimination of the arbitrary constants A, B and C from \[y=A+Bx+C{{e}^{-x}}\]leads to the differential equation [AMU 1999]
A)
\[{{{y}'}'}'-{y}'=0\] done
clear
B)
\[{{{y}'}'}'-{{y}'}'+{y}'=0\] done
clear
C)
\[{{{y}'}'}'+{{y}'}'=0\] done
clear
D)
\[{{y}'}'+{{y}'}'-{y}'=0\] done
clear
View Solution play_arrow
-
question_answer23)
The differential equation obtained on eliminating A and B from the equation \[y=A\cos \omega t+B\sin \omega t\] is [Karnataka CET 2000; Pb. CET 2001]
A)
\[{y}''=-{{\omega }^{2}}y\] done
clear
B)
\[{y}''+y=0\] done
clear
C)
\[{y}''+{y}'=0\] done
clear
D)
\[{y}''-{{\omega }^{2}}y=0\] done
clear
View Solution play_arrow
-
question_answer24)
If \[y=a{{x}^{n+1}}+b{{x}^{-n}},\] then \[{{x}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}\] equals to [RPET 2001]
A)
\[n(n-1)y\] done
clear
B)
\[n(n+1)y\] done
clear
C)
ny done
clear
D)
n2y done
clear
View Solution play_arrow
-
question_answer25)
The differential equation of all straight lines passing through the origin is [DCE 2002; Kerala (Engg.) 2002; UPSEAT 2004]
A)
\[y=\sqrt{x\frac{dy}{dx}}\] done
clear
B)
\[\frac{dy}{dx}=y+x\] done
clear
C)
\[\frac{dy}{dx}=\frac{y}{x}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer26)
\[y=a{{e}^{mx}}+b{{e}^{-mx}}\] satisfies which of the following differential equations [Karnataka CET 2002]
A)
\[\frac{dy}{dx}-my=0\] done
clear
B)
\[\frac{dy}{dx}+my=0\] done
clear
C)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{m}^{2}}y=0\] done
clear
D)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\] done
clear
View Solution play_arrow
-
question_answer27)
If \[{{x}^{2}}+{{y}^{2}}=1\] then \[\left( {y}'=\frac{dy}{dx},{y}''=\frac{{{d}^{2}}y}{d{{x}^{2}}} \right)\] [IIT Screening 2000]
A)
\[y{y}''-2{{({y}')}^{2}}+1=0\] done
clear
B)
\[y{y}''+{{({y}')}^{2}}+1=0\] done
clear
C)
\[y{y}''-{{({y}')}^{2}}-1=0\] done
clear
D)
\[y{y}''+2{{({y}')}^{2}}+1=0\] done
clear
View Solution play_arrow
-
question_answer28)
Differential equation of \[y=\sec ({{\tan }^{-1}}x)\] is [UPSEAT 2002]
A)
\[(1+{{x}^{2}})\frac{dy}{dx}=y+x\] done
clear
B)
\[(1+{{x}^{2}})\frac{dy}{dx}=y-x\] done
clear
C)
\[(1+{{x}^{2}})\frac{dy}{dx}=xy\] done
clear
D)
\[(1+{{x}^{2}})\frac{dy}{dx}=\frac{x}{y}\] done
clear
View Solution play_arrow
-
question_answer29)
The differential equation satisfied by the family of curves \[y=ax\cos \,\left( \frac{1}{x}+b \right)\], where a, b are parameters, is [MP PET 2003]
A)
\[{{x}^{2}}{{y}_{2}}+y=0\] done
clear
B)
\[{{x}^{4}}{{y}_{2}}+y=0\] done
clear
C)
\[x{{y}_{2}}-y=0\] done
clear
D)
\[{{x}^{4}}{{y}_{2}}-y=0\] done
clear
View Solution play_arrow
-
question_answer30)
The differential equation for which \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=c\] is given by [Karnataka CET 2003]
A)
\[\sqrt{1-{{x}^{2}}}\,\,dx\,\,+\sqrt{1-{{y}^{2}}}\,\,dy=0\] done
clear
B)
\[\sqrt{1-{{x}^{2}}}\,\,dy\,\,+\sqrt{1-{{y}^{2}}}\,\,dx=0\] done
clear
C)
\[\sqrt{1-{{x}^{2}}}\,\,dy\,\,-\sqrt{1-{{y}^{2}}}\,\,dx=0\] done
clear
D)
\[\sqrt{1-{{x}^{2}}}\,\,dx\,-\sqrt{1-{{y}^{2}}}\,\,dy=0\] done
clear
View Solution play_arrow
-
question_answer31)
If \[x=\sin t\], \[y=\cos pt\], then [Karnataka CET 2005]
A)
\[(1-{{x}^{2}}){{y}_{2}}+x{{y}_{1}}+{{p}^{2}}y=0\] done
clear
B)
\[(1-{{x}^{2}}){{y}_{2}}+x{{y}_{1}}-{{p}^{2}}y=0\] done
clear
C)
\[(1+{{x}^{2}}){{y}_{2}}-x{{y}_{1}}+{{p}^{2}}y=0\] done
clear
D)
\[(1-{{x}^{2}}){{y}_{2}}-x{{y}_{1}}+{{p}^{2}}y=0\] done
clear
View Solution play_arrow