Question

Resolva a equação diferencial y'(x) = xy por separação de variáveis.

Answer 1

$\frac{dy}{dx} = xy\\\\ \frac{1}{y}dy = xdx\\\\\int\frac{1}{y}dy =\int xdx\\\\ ln|y|=\frac{x^2}{2}+c_1\\\\e^{ln|y|} = e^{\frac{x^2}{2}+c_1}\\\\|y|=e^{c_1}*e^{\frac{x^2}{2}}\\\\\boxed{y=c*\sqrt{e^{x^2}}}\ \ \ \ \ (c\neq0)$