Question

The solution of the differential equation $x\frac{dy}{dx}+y=x^2+3x+2$ is

• A. $xy=\frac{x^3}{3}+\frac{3}{2}{x}^2+2x+c$
• B. $xy=\frac{x^4}{4}+x^3+x^2+c$
• C. $xy=\frac{x^4}{4}+\frac{3}{3}{x}^2+c$
• D. $xy=\frac{x^4}{4}+x^3+x^2+cx$

Answer 1

The correct option is A

$xy=\frac{x^3}{3}+\frac{3}{2}{x}^2+2x+c$

$x\frac{dy}{dx}+y=x^2+3x+2\Rightarrow \frac{dy}{dx}+\frac{y}{x}=x+3\frac{2}{x}$
Here $P=\frac{1}{x},Q=x+3+\frac{2}{x},$ therefore
$I.F.=e^{\int \frac{1}{x}dx}=x$
Now solve it.