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

Back To University Year 1 Physics Notes

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