# Solving differential equation using modified Euler's method.

Use the modified Euler's method to solve y' = -y +x + 2; y(0) =2 on the interval [0,1] with h = 0.1

Carry all computations to three decimal places.

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#### Solution Preview

Here f (x, y) = -y+x+2, x0 = 0 and y0 = 2, and we are to use h = 0.1. We begin by approximating the value of y at x1 = x0 + h =0.1. A first approximation y1(1) to this value is found using the formula,

y1(1) = y0 + h f (x0,y0) = 2.000 +0.1 (-2.000+0.000+2.000) = 2.000

We now find the second approximation y1(2).

Since f (x1,y1(1)) = f (0.100, 2.000) = -2.000+0.100+2.000 = 0.100

y1(2) = y0 + Â½ [f ...

#### Solution Summary

Solving differential equation using modified Euler's method.

We begin by approximating the value of y at x1 = x0 + h =0.1. A first approximation y1(1) to this value is found using the formula,

y1(1) = y0 + h f (x0,y0)