What is \(\text{d}y/\text{d}x\)?
What is the step size \(h\)? 1.000
How many particles should be shown? 800
Euler's method
Euler's method is a technique for approximately solving first-order differential equations. You pick a point and update the coordintes according to a rule that means it will follow the shape of the solution curve.
$$ y_{r + 1} = y_r + h \frac{\text{d}y}{\text{d}x}_r $$
You can either write your own function or use one of the examples below. The function should be written in JavaScript syntax in terms of \(x\) and \(y\). Common functions like \(\sin\), \(\cos\) and \(\text{abs}\) are included. Because it is JavaScript, it means you can't have implicit multiplication, so the code "100 + xy" wouldn't work but "100 + x*y" would.
You can also draw your own points by dragging with your finger or mouse.
Examples
- \(\frac{\text{d}y}{\text{d}x} = \frac{y}{x}\)
- \(\frac{\text{d}y}{\text{d}x} = -\frac{x}{y}\)
- \(\frac{\text{d}y}{\text{d}x} = 10\sin(x)\)
- \(\frac{\text{d}y}{\text{d}x} = \frac{x}{100}\)