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



Mini Physics

Administrator of Mini Physics. If you spot any errors or want to suggest improvements, please contact us. If you like the content in this site, please recommend this site to your friends!



Leave a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.