# Euler Method without using ODE solvers such as ode45

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KayLynn on 8 Feb 2014
Commented: Erin W on 22 Sep 2016
I am trying to write a code that will solve a first order differential equation using Euler's method. I do not want to use an ode solver but rather would like to use numerical methods which allow me to calculate slope (k1, k2 values, etc). I am given an equation with two different step values. I am not sure how to begin to write this in MATLAB. I have solved the equation by hand and am now trying to write a code that solves that equation.
The equation to be used is y’ +2y = 2 – e -4t.
y(0) = 1, which has an exact solution:
y(t) = 1 + 0.5 e -4t - 0.5 e -2t .
I did the following to solve numerically: 1+(0.5e^-4t) - (0.5e^-2(0)) y_n+1=1+0.1 and y_n+1=1+1(.001)
The step sizes are 0.1 and 0.001. (so my h in this example). The t values range from 0.1 to 5.0.
Any help is appreciated even if its an example pseudocode. Thank you

Amit on 8 Feb 2014
Edited: Amit on 8 Feb 2014
Given the equation:y' + 2y = 2 - 1e-4t The approximation will be: y(t+h) = y(t) +h*(- 2*y(t)+ 2 - e(-4t))
To write this: EDIT
y = 1; % y at t = 0
h = 0.001;
t_final = 0.1;
t = 0;
while (t < t_final)
y = y +h*(- 2*y+ 2 - exp(-4*t));
t = t + h;
end
Erin W on 22 Sep 2016
@James I did but I haven't been responded to yet :(