Problem 13 | Separation of Variables

$xy^3 \, dx + e^{x^2} \, dy = 0$

$\dfrac{xy^3 \, dx}{y^3 e^{x^2}} + \dfrac{e^{x^2} \, dy}{y^3 e^{x^2}} = 0$

$\dfrac{x \, dx}{e^{x^2}} + \dfrac{dy}{y^3} = 0$

$xe^{-x^2} \, dx + y^{-3} \, dy = 0$

$\displaystyle -\frac{1}{2} \int e^{-x^2} (-2x \, dx) + \int y^{-3} \, dy = 0$

$-\frac{1}{2} e^{-x^2} - \frac{1}{2} y^{-2} = -\frac{1}{2}c$

$e^{-x^2} + y^{-2} = c$           answer