# ODEs: Tangent Fields, Isoclines and Euler's Numerical Method

- Author:
- Micky Bullock

Input your ODE and press enter, or play with the tools for the default ODE.

Show Euler Particular Solution Curve: This uses Euler's method with approximate error correction to construct a particular solution through the tangent field (drag the blue point to set the boundary condition). (Euler's method is employed with step length = h. It is employed again with step length = 0.5h. The relationship is approximately linear; this provides an estimate for step length = 0)
Paint Tools: Colour the gradient field (x=-5..5, y=-5..5) as per the Key
colorlimit and pronunciation: use these to adjust the RGB color gradients; have a play
Depending on the speed of your computer, you may need to adjust spd (the paint speed) to ensure a smooth paint
Press ctrl-f to clear all paint
Particular solution curve algorithm may break down along curved asymptotes under certain conditions