$\frac{dy}{dx}=(1+2x)\sqrt[\phantom{2}]{y}$

$($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.