Question

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

• A. $y=\frac{x^{2}}{2}+C x$
• 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)

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