## Separable First-Order Differential Equations

A differential equation is separable if the variables can be separated:

F(y) dy = G(x) dx

The step towards solving the equation is to integrate both sides:

∫ F(y) dy = ∫ G(x) dx

Remaining step is to solve for y in terms of x (if possible). If it not possible to solve directly for x, the result should be written as an implicit format.

Example:

Solve the equation (x

^{2}+ 1) dx − 2y dy = 0Solution: