Question

The solution of differential equation $x\frac{dy}{dx}+2y=x^2$ is......

• A. $y=\frac{x^2+C}{4x^2}$
• B. $y=\frac{x^2}{4}+C$
• C. $y=\frac{x^4+C}{x^2}$
• D. $y=\frac{x^4+C}{4x^2}$

Answer 1

The correct option is D

$y=\frac{x^4+C}{4x^2}$

$y.e^{\int \frac{2}{x}dx}=\int x.e^{\int \frac{2}{x}dx}=\frac{x^4}{4}+c\Rightarrow y=\frac{x^4+c}{4x^2}$