69
MCQ (Single Correct Answer)
Which of the following is the general solution of $\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+y=0$ ?
A
$y=(A x+B) e^x$
B
$y=(A x+B) \mathrm{e}^{-x}$
C
$y=A e^x+B e^{-x}$
D
$y=A \cos x+B \sin x$
70
MCQ (Single Correct Answer)
The general solution of $\frac{d y}{d x}+y \tan x=\sec x$ is
A
$y \sec x=\tan x+C$
B
$y \tan x=\sec x+C$
C
$\tan x=y \tan x+C$
D
$x \sec x=\tan y+C$
71
MCQ (Single Correct Answer)
The solution of differential equation $\frac{d y}{d x}+\frac{y}{x}=\sin x$ is
A
$x(y+\cos x)=\sin x+C$
B
$x(y-\cos x)=\sin x+C$
C
$x y \cos x=\sin x+C$
D
$x(y+\cos x)=\cos x+C$
72
MCQ (Single Correct Answer)
The general solution of differential equation $\left(e^x+1\right) y d y=(y+1) e^x d x$ is
A
$(y+1)=k\left(e^x+1\right)$
B
$y+1=e^x+1+k$
C
$y=\log \left\{k(y+1)\left(e^x+1\right)\right\}$
D
$y=\log \left\{\frac{e^x+1}{y+1}\right\}+k$
73
MCQ (Single Correct Answer)
The solution of differential equation $\frac{d y}{d x}=e^{x-y}+x^2 e^{-y}$ is
A
$y=e^{x-y}-x^2 \mathrm{e}^{-y}+C$
B
$\mathrm{e}^y-\mathrm{e}^x=\frac{x^3}{3}+\mathrm{C}$
C
$\mathrm{e}^x+\mathrm{e}^y=\frac{x^3}{3}+\mathrm{C}$
D
$\mathrm{e}^x-\mathrm{e}^y=\frac{x^3}{3}+C$