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## Homework Statement

Use Euler's method with [tex]h = 1/2[/tex] to estimate [tex]y(1)[/tex] for the IVP:

[tex]y(0)=1[/tex] [tex]y'(t)=t^2-y(t)[/tex]

Assuming that [tex]|y(t)| \le 1[/tex] for [tex]0 \le t \le 1[/tex] determine the value of n needed to ensure that [tex]|E_n| \le 10^{-2}[/tex]

## Homework Equations

[tex]|E_n| \le \frac{T}{L}(e^{L(t_n-t_0)-1})[/tex]

## The Attempt at a Solution

The first part is easy enough:

[tex]y_1=y_0+f(t_0,y_0)h=1+f(0,1)(1/2)=1/2[/tex]

[tex]y_2=y_1+f(x_1,y_1)h=1/2-1/8=3/8[/tex]

[tex]\Rightarrow y(1)=3/8[/tex]

I'm having trouble with the second part. Could somebody help me out?