[list=1][*]If you're estimating solutions to a system of first order differential equations, adjust [code]f_1(x,y,t)[/code] as needed. Note: if you're only estimating solutions to a second order differential equation (by way of its systemification), then skip this step. [/*][*]Adjust [code]f_2(x,y,t)[/code] as needed. If you are estimating solutions to a second order differential equation, then this is the only thing you need to change. Previous lessons in this book discuss how to choose [code]f_2[/code] appropriately. Note that [code]x_1=x[/code] and [code]x_2=y[/code] in this program. Also note that no changes are needed to [code]f_1[/code] if representing a second order differential equation.[/*][*]Adjust [code]h[/code] to your desired step size.[/*][*]Adjust [code]x_{10}[/code] and [code]x_{20}[/code] to match your initial conditions.[/*][*]Unfortunately it's tricky to add more steps. To do so, select the entire final row of data, and drag the "Fill Handle" (blue box in the bottom right of a selected cell or cells) to extend the formula into more cells and calculate the desired number of steps.[/*][/list]If you're using this calculator to estimate solutions of a second order differential equation, the results are in column [code]B[/code].

At the outset, the above applet illustrates the numerical estimate of the solution to [br][br][math]y''-3y'-4y=2\sin\left(t\right);y\left(0\right)=2;y'\left(0\right)=3[/math][br][br]which has systemification[br][br][math]x_1'=x_2[/math][br][math]x_2'=4x_1+3x_2+2\sin\left(t\right)[/math][br][br]using [code]n=10[/code] steps of [code]h=0.1[/code] to arrive at an estimate of [code]y(1)[/code] and [code]y'(1)[/code], as well as all intermediate values of [code]y[/code] and [code]y'[/code] at multiples of 0.1. [br][br]Be sure to compare this calculator with the "by hand" calculations described in the previous lesson.