# To solve two 2nd order coupled differential equation using ODE45?

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Rohit Singh on 26 Sep 2021
Commented: Rohit Singh on 29 Sep 2021
I have the the following 2nd order differential equation that is needed to be solved.
..............(1)
....................(2)
The initial state are [3 9] for and respectively.
The time interval is [0: 0.05: 1] i.e 21 time steps.
The and are functions of time available for initial 20 time steps (can take as ones for working example).
I don't have any prior experince with ODE45 . Any guidance to solve this problem will be appreciated.

Alan Stevens on 26 Sep 2021
Replace each 2nd order ODE by two 1st order ODEs. e.g. set V1 = X1', V2 = X2', then V1' = (50*sin(f(t) - V1)*V2')/sin(f(t)), V2' = g(t) - etc.
You will also need initial conditions for V1 (X1') and V2 (X2') as well as for X1 and X2.
help ODE45 % for further details.
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Rohit Singh on 29 Sep 2021
Thank you @Star Strider for the guidance.

R2016a

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