Question

Solution of the differential equation $\frac{dy}{dx}+\frac{y}{x}=sinx$ is

• A. $x(y + cos\, x) = sin\, x + c$
• B. $x(y - cos\, x) = sin \,x + c$
• C. $xy\,cos\,x = sin \,x + c$
• D. $x(y + cos\, x) = cos \,x + c$

Answer 1

Answer: (A)

$\frac{dy}{dx}+\frac{y}{x}=sinx$
It is linear differential equation with
$I.F.=e^{\int \frac{1}{x}dx}=e^{logx}=x$
Now, solution is $y\cdot x=\int x\,sinx\,dx+c$
$\Rightarrow x\cdot y=-xcosx+sinx+c$
$\Rightarrow x\left(y+cosx\right)=sinx+c$