Solving multi-variable ODE
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Hello, I am having a hard time solving an ODE. Any help witll be grealy appreciated.
Below is the ODE i am trying to solve.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1298435/image.png)
As you can see, I am trying to solve for η, and
,
and
are just constants.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1298440/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1298445/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1298450/image.png)
The problem is that v(r) is a function of r which is defined over r= [0 1]. (and same for
)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1298455/image.png)
And of course i only need to solve η for r = [0 1].
I looked at many examples, but i could not find any that resembles my equation.
The initial conditions are η=0, and r ≈ 0.
Before you tell me that I can just solve it by integrating it both sides, I have solved it that way, but i just want to learn how to solve such ODEs without integrating it.
Thanks in advance!!
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Réponses (2)
Torsten
le 17 Fév 2023
Modifié(e) : Torsten
le 17 Fév 2023
If nu(r) is known, you have to insert the expressions for nu(r) and dnu/dr in your equation for eta.
If nu(r) is unknown, you must solve an additional equation for it.
And then you can apply ode45 to solve one equation for eta or two equations for eta and nu.
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