write code in python$($check bottom instruction$)$: Consider the following ODE:

$\frac{dy}{dx}-y=2,y(0)=1$

The analytic solution is given by $y(x)=3e^x-2.$ Let $h$ be the step size. Now using the

Euler and Runge$-$Kutta $($RK$)$ Methods, calculate $y(x=1),$ and estimate the error

rate for both methods separately using the formula: $e=\frac{y_{\text{c}\text{a}\text{l}\text{c}\text{u}\text{l}\text{a}\text{t}\text{e}\text{d}}-y_{\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}}{y_{\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}}.$

Here, at $x=1,$ we have $y_{\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}=3e-2.$ Now plot the error rate at $x=1$

vs step size for both Euler and RK methods in the same graph. Take

$h=0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}25,0\mathrm{.}5,1.($Use scipy.integrate.solve$\_$ivp to implement RK method.$)$