Euler's method
If you do not need to find an exact solution to the initial value problem for the initial value , you can use Euler's method to find a numerical solution. The interactive figure illustrates this method. You can change the initial value by dragging it. You can change the length of the step () by sliding the slider bar. The blue graph is the solution curve.
Spreadsheet Details
In the spreadsheet, the notation x(A) is the value of the the -coordinate of point A. The notation f(A2) means to evaluate function at the value in cell A2. Function is the (exact) solution of the differential equation.
Notice the formula in cell B3. The formula states the current y-value (B3) is equal to the previous y-value (B2) increased by how fast the y-value is changing in that time period (the derivative 1 – y becomes 1 – B2) times the length of the step (dx).
Developed for use with Thomas' Calculus, published by Pearson.