Differential Equations Test

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Differential Equations Test - 58

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Weekly Quiz Competition

Question 1
1 / -0

General solution of the differential equation (x+y-2) dy=(x+y) dx is

A
y+x=log(y-x+1)+c

B
y-x log (x+y-1)+c

C
y-2x=log (x+y-1)+c

D
y+2x=log (x+y+1)+c

Solution
Question 2
1 / -0

The solution of $$x^2dy-y^2dx+xy^2(x-y)dy=0$$ is?

A
$$ln\left|\dfrac{x-y}{xy}\right|=\dfrac{y^2}{2}+c$$

B
$$ln\left|\dfrac{xy}{x-y}\right|=\dfrac{x^2}{2}+c$$

C
$$ln\left|\dfrac{x-y}{xy}\right|=\dfrac{x^2}{2}+c$$

D
$$ln\left|\dfrac{x-y}{xy}\right|=x+c$$

Solution
Question 3
1 / -0

Solution of $$\left(1+xy\right)ydx+\left(1-xy\right)xdy=0$$ is

A
$$\log\dfrac{x}{y}+\dfrac{1}{xy}=c$$

B
$$\log\dfrac{x}{y}=c$$

C
$$\log\dfrac{x}{y}-\dfrac{1}{xy}=c$$

D
$$\log\dfrac{y}{x}-\dfrac{1}{xy}=c$$

Solution
Question 4
1 / -0

The general solution of the differential equation $$y-x\dfrac{dy}{dx}=y^{2}\cos x\left(1-\sin x\right)$$ is

A
$$y\left(\sin x+c\right)=\tan x+\sec x$$

B
$$y\left(\sin x+c\right)=\tan x-\sec x$$

C
$$\dfrac{x}{y}=\sin x+\dfrac{1}{4}\cos 2x+c$$

D
$$\dfrac{x}{y}=\sin x+\dfrac{1}{8}\cos 2x+c$$

Solution
Question 5
1 / -0

General solution of differential equation $$x^2dy + y(x + y)dx = 0$$ is

A
$$2x + y = Ax^2Y$$

B
$$2x - y = \dfrac{Ax^2}{y}$$

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

D
$$x - 2y = Ax^2y$$

Solution
Question 6
1 / -0

If $$y(t)$$ is solution of $$(t + 1) \dfrac{dy}{dt} - ty = 1, y(0) = -1$$, then $$y(1) =$$

A
$$\dfrac{1}{4}$$

B
$$-2$$

C
$$-\dfrac{1}{2}$$

D
$$\dfrac{1}{2}$$

Solution
Question 7
1 / -0

The solution of the Differential Equation $$(x+y)(dx-dy)=dx+dy$$ is

A
$$l\ n(x-y)=x+y+C$$

B
$$l\ n(x+y)=x-y+C$$

C
$$l\ n(x-y)=x-y-C$$

D
$$none\ of\ these$$

Solution
Question 8
1 / -0

The integrating factor of the equation $$y^{2}dx+(3xy-1)dy=0$$ is

A
$$y^{2}$$

B
$$y^{3}$$

C
$$\dfrac {1}{y^{2}}$$

D
$$\dfrac {1}{y^{3}}$$

Solution
Question 9
1 / -0

The solution of the differential equation $$\dfrac{dy}{dx}=\sec (x+y)$$ is

A
$$y-\tan\dfrac{x+y}{2}=c$$

B
$$y+\tan\dfrac{x+y}{2}=c$$

C
$$y+2\tan\dfrac{x+y}{2}=c$$

D
$$None\ of\ these$$

Solution
Question 10
1 / -0

The solution of differential equation $$dy/dx -y/x+\tan y/x$$ is:

A
$$x=C'\cos (y/x)$$

B
$$x=C'\sin (y/x)$$

C
$$x=C'\csc (y/x)$$

D
$$none\ of\ these$$

Solution