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

The general solution of the equation $\frac{d y}{d x}+\frac{1}{x} y=\frac{1}{x} e^x$

A

$y=x e^x+c$

B

$y=x e^x+c e^{-x}$

C

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

D

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

2
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation

$$ \left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x $$

A

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

B

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

C

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

D

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

3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Among the options given below from which option a differential equation of order two can be formed ?
A
All circles passing through origin
B
All parabolas passing through origin and having focus on X-axis
C
All the lines passing through the origin
D
All the hyperbolas of the form $x^2-y^2=K^2$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The differential equation for which $a x+b y=1$ is general solution is
A
$\frac{d y}{d x}=x+c$
B
$y \frac{d^2 y}{d x^2}+x=1$
C
$\frac{d^2 y}{d x^2}=0$.
D
$\frac{d^3 y}{d x^3}=0$
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