1
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the degree of the differential equation corresponding to the family of curves $y=a x+\frac{1}{a}$ (where $a \neq 0$ is an arbitary constant) is $r$ and it's order is $m$. Then, the solution of $\frac{d y}{d x}=\frac{y}{2 x}, y(\mathrm{l})=\sqrt{r+m}$ is

A

$y=3^x$

B

$y^2=3 x$

C

$x^2=3 y$

D

$y=3 \log x$

2
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $y+\cos x\left(\frac{d y}{d x}\right)-\cos ^2 x=0$ is

A

$(\sec x+\tan x) y=x+\cos x+c$

B

$(1+\cos x) y=(x+c) \cos x-\cos ^2 x$

C

$(1+\sin x) y=(x+c) \cos x-\cos ^2 x$

D

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

3
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $\frac{d y}{d x}+x y=4 x-2 y+8$ is

A

$y=4-c e^{-\frac{(x+2)^2}{2}}$

B

$y=8+c e^{-\frac{x^2}{2}-2 x}$

C

$y=c e^{-(x+2)^2}+x$

D

$y+2 x=c e^{-\frac{x}{2}-2 x}$

4
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $\left(x+2 y^3\right) \frac{d y}{d x}-y=0, y>0$ is

A

$y=x^3+c y$

B

$x=y^3+c y$

C

$y(1-x y)=c x$

D

$x(1-x y)=c y$

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