Variable Separable Differential Equation

A first order equation $\frac{dy}{dx} = f(x,y) $ is said to be variable separable if f(x,y) is of the form:$$ g(x)h(y) $$

Steps to solve $\frac{dy}{dx} = g(x)h(y) $:

1. Swap the variables around: $\frac{1}{h(y)}dy = g(x) dx$
2. Evaluate: $\int \frac{1}{h(y)} \, dy = \int g(x) \, dx$
3. You’re done! (Note: you might want to attempt to solve for y explicitly)

Back To First Order Differential Equations