# Solving System of 5 ODEs using ODE45

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Eira am 23 Okt. 2014
Kommentiert: Mikhail am 23 Okt. 2014
I have a 5 differential equations I am needing to solve. Three of the equations are second order while the other two are first order. I know how to write the code to solve a system of two first order ODEs, but I cannot seem to connect the concepts from that to what I am needing. I am trying to use the ode45 function. I don't really have any lines of code as matlab gives me errors on everything. I can supply the equations if needed.
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### Antworten (1)

Mikhail am 23 Okt. 2014
You can always get two first order ODE from one second order:
if you have 2nd order ODE for y(t), use y1=y(t), y2=y'(t)=dy/dt.
So you can use ode45 to solve system of 8 1st order equations.
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Mikhail am 23 Okt. 2014
In more details:
If your 2nd order ODE for y(t) is f(y'',y',y,t)=0, where ' is derivative, f - some function, you denote y1(t)=y(t) and y2(t)=y'(t) and get 2 1st order ODE's:
f(y2'(t),y2(t),y1(t),t)=0
y2'(t)=y1(t)

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