47
MCQ (Single Correct Answer)
The integrating factor of differential equation $\left(1-x^2\right) \frac{d y}{d x}-x y=1$ is
A
$-x$
B
$\frac{x}{1+x^2}$
C
$\sqrt{1-x^2}$
D
$\frac{1}{2} \log \left(1-x^2\right)$
48
MCQ (Single Correct Answer)
$\tan ^{-1} x+\tan ^{-1} y=C$ is general solution of the differential equation
A
$\frac{d y}{d x}=\frac{1+y^2}{1+x^2}$
B
$\frac{d y}{d x}=\frac{1+x^2}{1+y^2}$
C
$\left(1+x^2\right) d y+\left(1+y^2\right) d x=0$
D
$\left(1+x^2\right) d x+\left(1+y^2\right) d y=0$
49
MCQ (Single Correct Answer)
The general solution of $e^x \cos y d x-e^x \sin y d y=0$ is
A
$\mathrm{e}^x \cos y=k$
B
$\mathrm{e}^x \sin y=k$
C
$\mathrm{e}^x=k \cos y$
D
$\mathrm{e}^x=k \sin y$
50
MCQ (Single Correct Answer)
The degree of differential equation $\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3+6 y^5=0$ is
A
1
B
2
C
3
D
5
51
MCQ (Single Correct Answer)
The solution of $\frac{d y}{d x}+y=e^{-x}, y(0)=0$ is
A
$y=e^x(x-1)$
B
$y=x e^{-x}$
C
$y=x e^{-x}+1$
D
$y=(x+1) \mathrm{e}^{-x}$