Differential Equations Test

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Differential Equations Test - 57

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Weekly Quiz Competition

Question 1
1 / -0

Solution of $$(x+y-1)dx+(2x+2y-3)dy=0$$ is

A
$$y+x+log(x+y-2)=c$$

B
$$y+2x+log(x+y-2)=c$$

C
$$2y+x+log(x+y-2)=c$$

D
$$2y+2x+log(x+y-2)=c$$

Solution
Question 2
1 / -0

Solution of the differential equation $$dr=a\left( r\sin\theta d\theta-\cos\theta dr \right )$$ is

A
$$r\left( 1+a\cos { \theta } \right) =c$$

B
$$r\left( 1+a\cos { \theta } \right) =ac$$

C
$$r\left( 1-a\cos { \theta } \right) =c$$

D
$$r\left( 1-a\cos { \theta } \right) =ac$$

Solution
Question 3
1 / -0

The solution of $$\dfrac{xdy}{x^{2}+y^{2}}=\left(\dfrac{y}{x^{2}+y^{2}}-1\right)dx$$ is

A
$$y=x\cot(c-x)$$

B
$$\cos^{-1}u/x=-x+C$$

C
$$y=x\tan (c-x)$$

D
$$y^{2}/x^{2}=x\tan (c-x)$$

Solution
Question 4
1 / -0

Solution of the differential equation $$\cos{\,}x {\,}dy=y(\sin{\,}x-y)dx,0<x<\dfrac{\pi}{2}$$ is

A
y sec x$$=$$ tan x $$+$$ c

B
y sec x$$=$$ sec x $$+$$ c

C
y sec x$$=$$ (sec x $$+$$ c) y

D
sec x$$=$$ y (tan x $$+$$ c)

Solution
Question 5
1 / -0

The solution of the differential equation $$ydx-xdy+3x^2y^2e^{x^3} dx=0$$ is

A
$$\dfrac{x}{y}+e^{x^3}=c$$

B
$$\dfrac{x}{y}-e^x=c$$

C
$$\dfrac{x}{y}+ex^{x^3}-x^2y=c$$

D
$$\dfrac{x}{y}-e^{x^3}=c$$

Solution
Question 6
1 / -0

Solution of the equation $$(x+y)^2\dfrac{dy}{dx}=4,y(0)=0$$ is

A
$$y=2tan^{-1}\left(\dfrac{x+y}{2}\right)$$

B
$$y=4tan^{-1}\left(\dfrac{x+y}{4}\right)$$

C
$$y=4tan^{-1}\left(\dfrac{x+y}{2}\right)$$

D
$$y=2tan^{-1}\left(\dfrac{x+y}{4}\right)$$

Solution
Question 7
1 / -0

The solution of the differential equation $$\log\left(\dfrac {dy}{dx}\right)=4x-2y-2,y=1$$ when $$x=1$$ is

A
$$2e^{2y+2}=e^{4x}+e^{2}$$

B
$$2e^{2y-2}=e^{4x}+e^{2}$$

C
$$2e^{2y+2}=e^{4x}+e^{4}$$

D
$$3e^{2y+2}=e^{3x}+e^{2}$$
Question 8
1 / -0

Solution of the differential equation $$\dfrac{dy}{dx}=\dfrac{y(1+x)}{x(y-1)}$$ is

A
$$\log|xy|+x-y=C$$

B
$$\log|xy|-x+y=C$$

C
$$\log|xy|+x+y=C$$

D
$$\log|xy|-x-y=C$$

Solution
Question 9
1 / -0

the solution of $$ydx-xdy+3{ x }^{ 2 }{ y }^{ 2 }{ e }^{ { x }^{ 3 } }dx=0$$ is

A
$$\frac { x }{ y } +{ e }^{ { x }^{ 3 } }$$=C

B
$$\frac { x }{ y } -{ e }^{ { x }^{ 3 } }$$=0

C
$$-\frac { x }{ y } +{ e }^{ { x }^{ 3 } }$$=C

D
none of these

Solution
Question 10
1 / -0

The solution of the differential equation $$\left(x+2y^{3}\right)\dfrac{dy}{dx}=y$$ is

A
$$\dfrac{x}{y^{2}}=y+C$$

B
$$\dfrac{x}{y}=y^{2}+C$$

C
$$\dfrac{x^{2}}{y}=y^{2}+C$$

D
$$\dfrac{x}{y}=x^{2}+C$$

Solution