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
$\mathrm{e}^x-\mathrm{e}^y=\frac{x^3}{3}+C$
74
MCQ (Single Correct Answer)
The solution of differential equation $\frac{d y}{d x}+\frac{2 x y}{1+x^2}=\frac{1}{\left(1+x^2\right)^2}$ is
A
$y\left(1+x^2\right)=C+\tan ^{-1} x$
B
$\frac{y}{1+x^2}=C+\tan ^{-1} x$
C
$y \log \left(1+x^2\right)=C+\tan ^{-1} x$
D
$y\left(1+x^2\right)=C+\sin ^{-1} x$
75
The degree of the differential equation $\frac{d^2 y}{d x^2}+e^{d y / d x}=0$ is ............ .
Explanation
Given differential equation is
$$\frac{d^2 y}{d x^2}+e^{\frac{d y}{d x}}=0$$
Degree of this equation is not defined.