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
$y=(x+1) \mathrm{e}^{-x}$
52
MCQ (Single Correct Answer)
The integrating factor of differential equation $\frac{d y}{d x}+y \tan x-\sec x=0$ is
A
$\cos x$
B
$\sec x$
C
$e^{\cos x}$
D
$\mathrm{e}^{\sec x}$
53
MCQ (Single Correct Answer)
The solution of differential equation $\frac{d y}{d x}=\frac{1+y^2}{1+x^2}$ is
A
$y=\tan ^{-1} x$
B
$y-x=k(1+x y)$
C
$x=\tan ^{-1} y$
D
$\tan (x y)=k$