Slope Fields & ODE Visualizer
Visualize direction fields for ordinary differential equations. Click the canvas to place an initial condition and trace solution curves using Euler’s method.
Differential Equation
Click on the canvas to place an initial condition point
Properties
| ODE | -- |
| Solution Type | -- |
| Initial Condition | -- |
| Slope at IC | -- |
| Equilibrium | -- |
The Math Behind It
Slope Fields
- A slope field plots dy/dx = f(x, y) at many grid points
- Each short segment shows the slope at that point
- The direction field reveals solution behavior without solving the ODE
- Euler’s method approximates: yn+1 = yn + f(xn, yn)·Δx
- Smaller step size Δx gives more accurate curves
Common ODEs
- dy/dx = y: exponential growth/decay — y = Cex
- dy/dx = −y/x: family of circles centered at the origin
- dy/dx = x + y: exponential solutions shifted by linear terms
- dy/dx = sin(x): antiderivative — y = −cos(x) + C
- Equilibrium points: where dy/dx = 0 — solution curves flatten out
You're crushing it!