# How to create a function that can solve and graph Euler's equations

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OvercookedRamen on 21 Sep 2019
Commented: KALYAN ACHARJYA on 22 Sep 2019
Hey guys, I'm trying to create a function that can take a differential equation and show the numerical solution via graph using Euler's Method. I have the code and it works on it's own. I just can't figure out how to get it to a function format. I tried looking at the help page but it only confused me more. I know you need to give the function inputs in order for you to get outputs, I just can't figure out where they go inside the function. Here is the code, hopefully this helps explain it.
%Section 1: Single Differential Equations.
h=0.1; % step's size
N=10; % number of steps
y(1)=1;
for n=1:N
y(n+1)= y(n)+h*(-6*y(n));
x(n+1)=n*h;
end
plot(x,y); %plots the first soltuion
hold on
h1=0.001; % step's size
N1=1000; % number of steps
y1(1)=1;
for n1=1:N1
y1(n1+1)= y1(n1)+h1*(-6*y1(n1)); %-6y1 is the differential equation, dy/dx = -6y. I had to use y1 because y is already used.
x1(n1+1)=n1*h1;
end
plot(x1,y1); % plots the second numerical solution
hold on
x3=0:0.001:1;
y3=exp(-6.*x3); %This is the solution to dy/dx = -6y
plot(x3,y3); % plots the exact solution to this differential equation
legend('h=0.1','h=0.001','Exact');

KALYAN ACHARJYA on 22 Sep 2019
I have the code and it works on it's own. I just can't figure out how to get it to a function format.
function plot_test()
data=input('Please enter how many numerical solution going to plot: ');
for i=1:data
h=input('Enter the Step size: ');
N=input('Number of Steps: ');
y(1)=1;
for n=1:N
y(n+1)= y(n)+h*(-6*y(n));
x(n+1)=n*h;
end
plot(x,y); %plots the first soltuion
hold on;
end
x3=0:0.001:1;
y3=exp(-6.*x3); %This is the solution to dy/dx = -6y
plot(x3,y3); % plots the exact solution to this differential equation
legend('h=0.1','h=0.001','Exact');
end
Command Window: Hope it helps!
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KALYAN ACHARJYA on 22 Sep 2019
It's my pleasure @Caleb