Question: numerical solution to a non-linear system of equations including derivatives


is there any way to solve a system like (d denotes the derivates):







If it were possible to solve the first two equations analytically, this would give me x1 and x2 depending on y1 and y2. Then I would insert this into the last two equations and solve them for y1 and y2. However, all equations are non-linear (and there are more than mentioned here) so that I don't get an analytical solution. The problem with numerical calculations is that I can't calculate the derivatives without having solved the first two equations analytically, i.e. I can't transform it into an ordinary system of four nonlinear equations. Is there any possibility to solve the system numerically anyway?

I would be very very grateful for any suggestions, since I have been struggling with this for several weeks now.

Thanks a lot,


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