Question

The general solution of the differential equation $x{y}^{\prime }+y=x^2,x>0$ is

• A. $y=\frac{x^2}{2}+Cx$
• B. $y=\frac{x^3}{3}+C$
• C. $y=\frac{x^2}{3}+C$
• D. $y=\frac{x^3}{3}+\frac{C}{x}$
• E. $y=\frac{x^2}{3}+\frac{C}{x}$

Answer 1

Answer: (E)

$\frac{dy}{dx}+\frac{y}{x}=x$
$I\cdot F=e^{\int \frac{1}{x}dx}=e^{\log x}=x$
$yx=\int x\cdot x\cdot dx$
$yx=\frac{x^3}{3}+C$
$y=\frac{x^2}{3}+\frac{c}{x}$