Consider the differential equation dy$/$dx$=2$x$,$ with initial condition y$(0)=4.$

a$)$ use linear approximation $($Euler$$s method$)$ with two steps to estimate y when x$=1$: y$(1)$~~

b$)$ now use four steps: y$(1)$~~

c$)$ what is the solution to this differential equation $($with the given condition$)?$

y$=$

d$)$ what is the magnitude of the error in the two Euler approximations you found?

Magnitude of error with $2$ steps:

Magnitude of error with $4$ steps: