Summary of Separable Equations

Essential Concepts

  • A separable differential equation is any equation that can be written in the form y=f(x)g(y)y=f(x)g(y).
  • The method of separation of variables is used to find the general solution to a separable differential equation.

Key Equations

  • Separable differential equation

    y=f(x)g(y)
  • Solution concentration

    dudt=INFLOW RATEOUTFLOW RATE
  • Newton’s law of cooling

    dTdt=k(TTs)
Glossary
autonomous differential equation
an equation in which the right-hand side is a function of y alone
separable differential equation
any equation that can be written in the form y=f(x)g(y)
separation of variables
a method used to solve a separable differential equation