Solve separable first-order ODEs dy/dx = g(x)·h(y) numerically with RK4.
A separable ODE has the form dy/dx = g(x)·h(y), meaning the right-hand side factors into a function of x alone times a function of y alone. Theoretically, ∫dy/h(y) = ∫g(x)dx + C. This calculator solves it numerically using RK4, which works even when the antiderivatives have no closed form. Enter g(x) using x, and h(y) using x or y as the variable.
Separable form
dy/dx = g(x) · h(y)
Analytical approach
∫ dy/h(y) = ∫ g(x) dx + C
An ODE is separable when dy/dx can be written as a product of a function of x alone and a function of y alone: dy/dx = g(x)·h(y).
While separable equations can theoretically be solved by integration, the integrals may not have closed-form solutions. Numerical methods always work.