1
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solutions of the differential equation $x \log x d y=(x \log x-y) d x$ is

A

$(x-y) \log x+x=C$

B

$x-y=\frac{x}{\log x}+C$

C

$y-x=\frac{x}{\log x}+C$

D

$(y-x) \log x+x=C$

2
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x$ is

A

$\cos \left(\frac{y}{x}\right)=\log |x|+C$

B

$\cos \left(\frac{y}{x}\right)=\frac{1}{x}+C$

C

$\cos \left(\frac{x}{y}\right)=\log |y|+C$

D

$\cos \frac{y}{x}=\frac{2}{x}+C$

3
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $\cos (x+y) d y=d x$ is

A

$y=\tan \left(\frac{x+y}{2}\right)+C$

B

$y=\sec \left(\frac{x+y}{2}\right)+C$

C

$y=x \sec \left(\frac{y}{x}\right)+C$

D

$y=-\cos ^{-1}\left(\frac{y}{x}\right)+C$

4
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $A x^3+B x y=4$ ( $A$ and $B$ are arbitrary constants) is the general solution of the differential equation $F(x) \frac{d^2 y}{d x^2}+G(x) \frac{d y}{d x}-2 y=0$, then $F(l)+G(l)=$

A

1

B

0

C

4

D

9

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