The solution of the differential equation $x\frac{dy}{dx}+2y=x^2$ is : (C is constant of integration )
Answer & explanation
Correct answer: option 1
$x\frac{dy}{dx}+2y=x^2$ so $\frac{dy}{dx}+\frac{2}{x}y=x$ ...(1)
so $I.F. = e^{\int\frac{2}{x}dx}=e^{ln|x^2|=x^2}$
Eqn. (1)
$⇒x^2\frac{dy}{dx}+2xy=x^3$ Integrating wrt x
$x^2y=\frac{x^4}{4}+C$