Question

xy' - (x+2)y = 0, x0 = 0

Answer 1

$xy' - (x+2)y = 0$

separate variables : $\frac{dy}{y} = \frac{x+2}{x} dx \Rightarrow d(ln(y)) = (1 + \frac{2}{x})dx$

integrate : $ln(y) = x + 2\cdot ln(x) + const$ , $y = x^2 \cdot e^{x} \cdot C$ , where C = const

ANSWER : $y = x^2 \cdot e^{x} \cdot C$ , where C = const