What is a solution to the differential equation (x^2)(e^y)dy/dx=4?

Aug 2, 2016

$y = \ln \left(C - \frac{4}{x}\right)$

Explanation:

We can separate the variables:

${x}^{2} {e}^{y} \frac{\mathrm{dy}}{\mathrm{dx}} = 4 \text{ "=>" } {e}^{y} \mathrm{dy} = 4 {x}^{-} 2 \mathrm{dx}$

Integrate both sides:

$\int {e}^{y} \mathrm{dy} = 4 \int {x}^{-} 2 \mathrm{dx} \text{ "=>" "e^y=-4/x+C" "=>" } y = \ln \left(C - \frac{4}{x}\right)$