-
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
View Solution play_arrow