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

The general solution of the differential equation $\frac{d y}{d x}+\frac{\sec x}{\cos x+\sin x} y=\frac{\cos x}{1+\tan x}$ is

A

$(\cos x+\sin x) y=\sin x+C$

B

$(\cos x+\sin x) y=\cos x+C$

C

$(1+\tan x) y=\cos x+C$

D

$\sec x(\cos x+\sin x) y=\sin x+C$

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

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

A

$\log \left|\frac{y^2-2 x^2}{x^2}\right|+\sqrt{2} \log \left|\frac{y-\sqrt{2} x}{y+\sqrt{2} x}\right| +2 \sqrt{2} \log |x|=C $

B

$\sqrt{2} \log \left|\frac{y^2-2 x^2}{x^2}\right|+\log \left|\frac{y-\sqrt{2} x}{y+\sqrt{2} x}\right| +2 \sqrt{2} \log |x|=C $

C

$\sqrt{2} \log \left|\frac{y^2+2 x^2}{x^2}\right|+\log \left|\frac{y+\sqrt{2} x}{y-\sqrt{2} x}\right| +2 \sqrt{2} \log |x|=C $

D

$\log \left|\frac{2 x^2-y^2}{x^2}\right|+\sqrt{2} \log \left|\frac{y+\sqrt{2} x}{y-\sqrt{2} x}\right| +\log |x|=C $

3
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

$y=3 \log x$

4
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

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

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