55
MCQ (Single Correct Answer)
$y=a e^{m x}+b e^{-m x}$ satisfies which of the following differential equation?
A
$\frac{d y}{d x}+m y=0$
B
$\frac{d y}{d x}-m y=0$
C
$\frac{d^2 y}{d x^2}-m^2 y=0$
D
$\frac{d^2 y}{d x^2}+m^2 y=0$
56
MCQ (Single Correct Answer)
The solution of differential equation $\cos x \sin y d x+\sin x \cos y d y=0$ is
A
$\frac{\sin x}{\sin y}=C$
B
$\sin x \sin y=C$
C
$\sin x+\sin y=C$
D
$\cos x \cos y=C$
57
MCQ (Single Correct Answer)
The solution of $x \frac{d y}{d x}+y=e^x$ is
A
$y=\frac{\mathrm{e}^x}{x}+\frac{k}{x}$
B
$y=x e^x+C x$
C
$y=x e^x+k$
D
$x=\frac{e^y}{y}+\frac{k}{y}$
58
MCQ (Single Correct Answer)
The differential equation of the family of curves $x^2+y^2-2 a y=0$, where $a$ is arbitrary constant, is
A
$\left(x^2-y^2\right) \frac{d y}{d x}=2 x y$
B
$2\left(x^2+y^2\right) \frac{d y}{d x}=x y$
C
$2\left(x^2-y^2\right) \frac{d y}{d x}=x y$
D
$\left(x^2+y^2\right) \frac{d y}{d x}=2 x y$
59
MCQ (Single Correct Answer)
The family $Y=A x+A^3$ of curves will correspond to a differential equation of order
A
3
B
2
C
1
D
not defined