# Solve Differential Equation dy/dx=xe^-y

In this tutorial we shall evaluate the simple differential equation of the form $\frac{{dy}}{{dx}} = x{e^{ - y}}$, and we shall use the method of separating the variables.

The differential equation of the form is given as

Separating the variables, the given differential equation can be written as

With the separating the variable technique we must keep the terms $dy$ and $dx$ in the numerators with their respective functions.

Now integrating both sides of the equation (i), we have

Using the formulas of integration $\int {{e^x}dx = {e^x}}$ and $\int {{x^n}dx = \frac{{{x^{n + 1}}}}{{n + 1}}}$, we get

This is the required solution of the given differential equation.