# Solving a system of ODE with BCs

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Elia Paini on 20 Apr 2021
Commented: Elia Paini on 24 Apr 2021
Hi, I'm trying to solve a system of 2 ODE with boundary conditions.
The integration variable is r, which is the sferical coordinate (radius of a sphere). At the end of the simulation I should get the values of A and B as a functions of r, where the maximum value of r is 1.
k,c,a,b are constants.
The system is as follows:
Equations:
BCs:
I converted the system to first order one, as follows:
Equations:
BCs:
Y3(0)=Y4(0)=0
Y1(1)=a
Y2(1)=b
How can I solve it?
Thank you!

Divija Aleti on 23 Apr 2021
Hi Elia,
The following link gives an example of how to solve a system of two first-order differential equations with boundary conditions. Similarly, you can solve for your converted system of four first order differential equations.
Hope this helps!
Regards,
Divija
Elia Paini on 24 Apr 2021
I tried to use the way you suggested me, but Matlab can't find a solution. The message is as follows:
Warning: Unable to find symbolic solution.
I think that, because the complexity of the system, bvp4c must be used. In this way, results are correct.