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**Question:** Consider the initial value problem $\frac{dy}{dt}=\alpha t^{\alpha - 1}, y(0)=0$, where $\alpha > 0$. The true solution is $y(t)=t^{\alpha}$. Use the Euler method to solve the initial value problem for $\alpha = 2.5,1,5,1.1$ with stepsize $h=0.2,0.1,0.05$. 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:

$0 \leq t \leq b$, with $N = (b-0)/0.2 = 5b$ for $h=0.2$, 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.