How can we use Euler's method to approximate the solutions for the following IVP below: y' = -y + ty^{1/2},\text{ with }1 \leq t \leq 2,\ y(1) = 2, and with $h = 0.5$
The main concern is the organization, i.e., set up of it for this particular example.
And, if the actual solution to the IVP above is: $y(t) = (t-2+\sqrt{2} \mathrm{e} \cdot \mathrm{e}^{-t/2})^2$, then, how to compare the actual error and compare the error bound?
Thanks