$.$ Euler Function

Create a file called euler.m that contains a function of the form

function $[$t$,$ y$]=$ euler$($f$,$ t$0,$ y$0,$ tn$,$ N$)$

This function should accept

$$ f: an anonymous function $($help on anonymous functions$)$ of t and y that describes the differential equation,

such that y

$=$ f$($t$,$ y$)$

$($use f $=$ @$($t$,$y$)...$ to define it$,$ but that comes later$)$

$$ t$0,$ y$0$: the initial condition

$$ tn: the t value where the approximation should end

$$ N: the number of steps used to get from t$0$ to tn

It should return

$$ t: an array containing N $+1$ values, evenly spaced from t$0$ to tn

$$ y: an array representing the solution to the differential equation $($the final value should be y$($tn$))$

Start by using t$0,$ tn$,$ and N to calculate the step size h$,$ then use that to generate the t array. Once you have

that, initialize the y array $($I usually start by creating an array of zeros of the right size$).$

Then use a for loop to fill in the values in the y array, using the formula for Euler$$s method $($inside the loop,

calculate the value of the derivative at that point and use that to get the next y value$).$