Example 08

The Do Command

GIVEN: A First Order ODE

y'=f(x,y)=-y+sinx
x0=0
y0=1

REQUIRED: Solve using the Euler's approximation.

SOLUTION:Generate example08.nb

Clear[f, x, y];

f[x_, y_] = -y + Sin[x];

x0=0;

y0= 1;

h = 0.01;

n=10;

x=x0;

y=y0;

output = {{x, y}};

Do[y=y+h*f[x, y];

x = x + h;

output = Append[output, {x, y}], {i, 1, n}];

ListPlot[output, PlotJoined -> True];

Homework:

Change the initial condition

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