# Subtracting the two resulting graghs of my ode program

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MA on 6 Jul 2016
Commented: MA on 7 Jul 2016
I have two second order differential equations. I solved them with Ode45, but I want to subtract the two resulting answers from each other and plot the subtraction of the one answer from another one. How can I do that???
function dy=function1(t,y)
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=sin(t)-y(1);
end
function dy=function2(t,y)
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=(t^2)-2*y(1)-y(2);
end
[T,Y]=ode45(@function1,[0 10],[0 0]);
[M,X]=ode45(@function2,[0 10],[0 0]);
plot(T,Y(:,1),M,X(:,1))
I want to plot X(:,1)-Y(:,1)???

Kelly Kearney on 6 Jul 2016
You can either change the second input of both ode45 calls to specify specific time values to output:
tspan = linspace(0,10,100);
[T,Y]=ode45(@function1,tspan,[0 0]);
[M,X]=ode45(@function2,tspan,[0 0]);
(Here, T, M, and tspan will be equal).
Or, you could keep your original input but interpolate both output timeseries to the same grid:
y2 = interp1(T, Y, tspan);
x2 = interp1(M, X, tspan);
plot(tspan, y2(:,1)-x2(:,1));
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MA on 7 Jul 2016
Thank you very much :)