An initial value problem, IVP is defined by a nonlinear autonomous first order differential equation and initial condition given by:

$\frac{dy}{dt}=3yln(\frac{10}{y}),y(0)=2$

The analytical solution for the IVP is given as:

$y(t)=\frac{10}{5^{\text{e}\text{x}\text{p}(-3t)}}$

Design, write and debug computer codes in either python, Matlab, or any other language you wish $($even EXCEL$)$ to do the following:

Obtain a solution to this DE using Euler's method using $h=t=0\mathrm{.}2$

Obtain a solution to this DE using Euler's method using $h=t=0\mathrm{.}1$

Obtain the analytic solution $($EQ $2)$ spaced at $t=0\mathrm{.}1$

The time interval for the solutions is $0,4$

If coding $($not EXCEL$)$ you should write a function called" diff$1$; the prototype function is something like: $dy=$diffl$(t,y)$ this form is generally used in various languages to access solvers $-$and is good practice. Use this to implement Euler's algorithm $($see class notes$).$ You put in $y$ and $t$ for each iteration.