# Implementing Euler's method for a 1D system

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Kristina on 3 Oct 2022
Commented: Torsten on 3 Oct 2022
I'm having trouble implementing euler's method for 𝑓(𝑥) = 𝑥^3 + 𝑥^2 − 12𝑥. I originally plotted the function just fine using this script:
x = [-5:0.1:5];
y = x.^3 + x.^2 - 12*x;
plot(x,y)
grid on.
Then when I try to implement euler's method to this function, I'm not receiving the same graph and am confused why. If I change anything in the x constraint it says my arrays are incorrect. If I change N for my number of steps it says incorrect arrays. And anything I put into my initial condition y(1) alters where the graph ultimately lays but never correctly on the roots.
h=0.1;
x=-5:h:5;
N=100;
y=zeros(size(x));
y(1)=0;
n=numel(y);
for n=1:N
dydx=3*x(n).^2+2*x(n)-12;
y(n+1)=y(n)+dydx*h;
end
plot(x,y);
grid on;
I did follow the basic steps for implementing euler's method that I am aware of, but it's not creating the graph I expect.
Ultimately I was supposed to plot the original function, then implement the 1D system using euler's method and x(t). But I can't get the code to run correctly for just the 1D system alone, let alone x(t).

KSSV on 3 Oct 2022
h=0.1;
x=-5:h:5;
y=zeros(size(x));
y(1)=0;
for n=1:length(x)-1
dydx=3*x(n).^2+2*x(n)-12;
y(n+1)=y(n)+dydx*h;
end
plot(x,y);
grid on;
Torsten on 3 Oct 2022
Well, I don't understand what you mean, but you're welcome ! :-)