Answer to Question #263625 in Differential Equations for Acestitches

Question

dy/dx=xe^x/(e^y+x^2e^y)

Answer 1

$\frac{dy}{dx}=\frac{xe^x}{\left(e^y+x^{\mathrm{2}}e^y\right)} \\ \\ \frac{dy}{dx}=\frac{xe^x}{e^y\left(\mathrm{1}+x^{\mathrm{2}}\right)} \\ \\ e^ydy=\frac{xe^x}{\left(\mathrm{1}+x^{\mathrm{2}}\right)}dx \\ \\ \int{e^ydy\ \ =\ \ \ \int{\frac{xe^x}{\left(\mathrm{1}+x^{\mathrm{2}}\right)}dx}} \\ \\ e^y=\frac{e^i}{\mathrm{2}}Ei\mathrm{(}x-i\mathrm{)}\ \ +\ \ \ \frac{e^{-i}}{\mathrm{2}}Ei\mathrm{(}x+i\mathrm{)}{}{}{}{}{}\ \ +\ \ C \\ \\ Ei\ \ \ \ is\ \ \ the\ \ \mathrm{exp}onential\ \ function\ \ \ \ and\ \ \ i\ \ \ \ \ is\ \ \ the\ \ complex\ \ number \\$