$(04)$ Given the initial$-$value problem

$y^{\text{'}}=\frac{2}{t}y+t^2{e}^t,1t2,y(1)=0$

With exact solution $y(t)=t^2(e^t-e).$

a$.$ Use Euler's method with $h=0\mathrm{.}1$ to approximate the solution and compare it with the actual values of $y.$

b$.$ Use Taylor's method of order $2$ with $h=0\mathrm{.}1$ to approximate the solution and compare it with the actual values of $y.$