I have a problem on which I need to apply Euler's method - EXCEPT that I don't have one of the crucial components. Question and my thoughts below:

**Question:** Consider the initial value problem $\displaystyle $dy/dt=\alpha t^{\alpha - 1}, y(0)=0$$, where $\displaystyle $\alpha > 0$$. The true solution is $\displaystyle $y(t)=t^{\alpha}$$. Use the Euler method to solve the initial value problem for $\displaystyle $\alpha = 2.5,1,5,1.1$$ with stepsize $\displaystyle $h=0.2,0.1,0.05$$. Compute the solution errors at the nodes, and determine numerically the convergence orders of the Euler method for these problems.

**My thoughts:** I don't have the "interval" for t! I tried setting the problem up as follows:

$\displaystyle $0 \leq t \leq b$$, with $\displaystyle $N = (b-0)/0.2 = 5b$$ for $\displaystyle $h=0.2$$, but wasn't able to get anything conclusive.

Should I try $b = 1$, so that t is restricted to a range in which it shrinks?

Thanks for any help.