Mark (√) against the correct answer in the following: The general solution of the DE $\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y} \cot \mathrm{x}=2 \cos \mathrm{x}$ is A. $(y+\sin x) \sin x=C$ B. $(y+\cos x) \sin x=C$ C. $(y-\sin x) \sin x=c$ D. None of these

Home » Mark (√) against the correct answer in the following: The general solution of the DE is A. B. C. D. None of these

Mark (√) against the correct answer in the following: The general solution of the DE $\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y} \cot \mathrm{x}=2 \cos \mathrm{x}$ is
A. $(y+\sin x) \sin x=C$
B. $(y+\cos x) \sin x=C$
C. $(y-\sin x) \sin x=c$
D. None of these

CBSE | Class 12 | Linear Differential Equations | Maths | RS Aggarwal

Mark (√) against the correct answer in the following: The general solution of the DE $\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y} \cot \mathrm{x}=2 \cos \mathrm{x}$ is
A. $(y+\sin x) \sin x=C$
B. $(y+\cos x) \sin x=C$
C. $(y-\sin x) \sin x=c$
D. None of these

Solution:

$\frac{d y}{d x}+y \operatorname{Cot} x=2 \operatorname{Cos} x$
Comparing with $\frac{d y}{d x}+P y=Q$
Integrating factor is $e^{\int \cot x d x}=\operatorname{Sin} x$
General solution is $y \sin x=\int 2 \operatorname{Cos} x \operatorname{Sin} x d x+C$
$y \sin x=(\operatorname{Sin} x)^{2}+C$
$(y-\sin x) \sin x=C$