Using Python: Solve the following equation numerically using the forward Euler method

$($du$)/($dt$)=$t$^(2)-10$ with the initial condition u$(0)=50$

As part of the solution process converge the solution by decreasing the step

size

You can determine the solution by taking the root$-$mean$-$square of the error

with respect to the exact solution. You will need to calculate the solution to

this differential equation. Then for each step size h$,$ you can calculate the

root$-$mean$-$square of the error. Once the root$-$mean$-$square of the error is less

than the accuracy of the solution, your result is converged. Choose a time

grid say from $0$ to $20.$

Once you have this working, try solving using the Forward Euler method,

$($du$)/($dt$)=$u$*$cos$($t$)$ with the initial condition u$(0)=1,$ and using a mesh from $0,10.$