An ODE dy dx = F(x, y) is separable if we can write F(x, y) = f(x)g(y) for some functions f(x), g(y). x2 9 + y2 4 = K, (K = C/36) which describes a 'family' of ellipses.

How do you know if an ode is separable?

A first-order differential equation is said to be separable if, after solving it for the derivative, dy dx = F(x, y) , the right-hand side can then be factored as “a formula of just x ” times “a formula of just y ”, F(x, y) = f (x)g(y) .

What does it mean for an ode to be separable?

Simply put, a differential equation is said to be separable if the variables can be separated. That is, a separable equation is one that can be written in the form. Once this is done, all that is needed to solve the equation is to integrate both sides.