# solveODE() Function & Examples

Use the solveODE() numeric function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

## solveODE

#### solveODE(func, tspan, y0)

#### solveODE(func, tspan, y0, options)

Try it yourself:

```calculio
f(t,y) = y
tspan = [0, 4]
solveODE(f, tspan, 1)
solveODE(f, tspan, [1, 2])
solveODE(f, tspan, 1, { method:"RK23", maxStep:0.1 })
```

[derivative](https://calcul.io/function/derivative/index.md)

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## solveODE(): Solving Ordinary Differential Equations

**solveODE()** solves an ordinary differential equation numerically from a model and initial conditions. It is useful for motion, population models, circuits, and dynamic systems.

## Model inputs matter

Specify the derivative rule, independent-variable interval, and initial state clearly. Numerical solutions depend on step size and tolerance; compare results at refined settings before trusting sensitive conclusions. Use [derivative()](https://calcul.io/function/derivative/index.md) for symbolic differentiation, not as a replacement for an ODE solve.

Inspect output shape with [size()](https://calcul.io/function/size/index.md), summarize trajectories with [mean()](https://calcul.io/function/mean/index.md) where appropriate, and use [abs()](https://calcul.io/function/abs/index.md) for error magnitude checks.

[All functions](https://calcul.io/functions/index.md)