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

If $y=A t^2+\frac{B}{t}$ ( $A, B$ are parameters) is general solution of the differential equation $f(t) y^{\prime \prime}(t)+g(t) y^{\prime}(t)+h(t) y=0$ then $2 f(t)+t^2 h(t)=$

A

$g(t)-h(t)$

B

$g(t)+f(t)$

C

$g(t) f(t)$

D

$(f(t))^{g( t)}$

2
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $(2 x-y)^2 d y-2(2 x-y)^2 d x-2 d x=0$ is

A

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

B

$(2 x-y)^3+4 y=C$

C

$(2 x-y)^3+6 x=C$

D

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

3
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

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

4
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

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

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