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The graph at the right shows the function sin t. We want to investigate the differential equation

T ' = k(sin t - T).

The x-axis in this graph is used for the variable t and the y-axis is used for the variable T. The x-axis runs from 0 to 2 pi and the y-axis runs from -2 to +2.

For each value of t and T the right hand side of this differential equation indicates the slope of the solution that passes through this point. Click anyplace inside the graph. A dot will appear at the point and a line will be drawn indicating the slope determined by the right hand side of the differential equation. You can click on as many different points as you want. You can clean the graph by clicking on the grey border.

Euler's Method in Pictures
From Multivariable Calculus, Linear Algebra, and Differential Equations in a Real and Complex World
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From Multivariable Calculus, Linear Algebra, and Differential Equations in a Real and Complex World