$(9\mathrm{.}1)$ Solve the following problems in $0t5$ using the forward Euler method with $h=0\mathrm{.}5$ by hand calculation.

Repeat the same with $h=0\mathrm{.}01$ by using a computer $($write a short program yourself$).$ Evaluate the errors

$($a$)y^{\text{'}}+ty=1,y(0)=1$

matlab octave

$($b$)y^{\text{'}}+3y=e^{-1},y(0)=1$

$($c$)y^{\text{'}}=(t2-y),y(0)=0\mathrm{.}5$

$($d$)y^{\text{'}}+y|y|=0,y(0)=1$

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