Using Python code $,$u

se the modified Euler method with $$t $=1$ and with two corrections $($one correction,

one recorrection$)$ per step to find x$(1)$ and y$(1)$ for the initial value problem

$$

$$

dx

dt

$=$ t $+$ x $$ y$,$ x$(0)=1$

dy

dt

$=$ y $$ x$2,$ y$(0)=0$