Problem

Solve the following problem over the interval from x $=0$ to $1$ using a step size of

$0\mathrm{.}25$ where y$(0)=1.$

$$

$$

$=(1+2)$

$($a$)$ Analytically.

$($b$)$ Euler$$s method.

$($c$)$ Heun$$s method with corrector

$($do only one iteration for each step$).$

$($d$)$ Midpoint method.

$($e$)$ Ralston$$s method.

$($f$)$ Fourth$-$order RK method

$($g$)$ Display all your results on the same graph and comment on the accuracy.

Develop a code or an excel sheet for the calculations.