Separable Equation Solver
Solve separable first-order ODEs dy/dx = g(x)·h(y) numerically with RK4.
Inputs
Function of x only.
Function of y only. dy/dx = g(x)·h(y).
y(target x)
1.64872127
Steps used
200
Step by step
Values used
g(x) factor = x; h(y) factor = y; Initial x₀ = 0; Initial y₀ = 1; Target x = 1; Steps = 200
Separable form
dy/dx = g(x) · h(y)
Analytical approach
∫ dy/h(y) = ∫ g(x) dx + C
y(target x)
= 1.64872127
Steps used
= 200
How it works
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.
Formulas
Separable form
dy/dx = g(x) · h(y)
- g(x)
- Function of x only
- h(y)
- Function of y only
Analytical approach
∫ dy/h(y) = ∫ g(x) dx + C
- C
- Integration constant from initial condition
Frequently Asked Questions
What makes an ODE separable?
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).
Why use numerical methods for separable equations?
While separable equations can theoretically be solved by integration, the integrals may not have closed-form solutions. Numerical methods always work.