How to solve a transcendental differential equation?

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Brian Camilo Gomez Leon
Brian Camilo Gomez Leon on 28 Oct 2020
Answered: Rohit Pappu on 16 Mar 2021
Hi,
I have a set of differential equations, something like this:
c1 = F(y1,y1',y1'',y2,y2',y2'') + k1*sin(G(y1,y1',y1'',y2,y2',y2''))+k2*sin(H(y1,y1',y1'',y2,y2',y2''))
c2 = k3*cos(G(y1,y1',y1'',y2,y2',y2''))+k4*cos(H(y1,y1',y1'',y2,y2',y2''))
where F,G and H are linear equations depending of y1, y2 and their derivatives; c1, c2, k1, k2, k3, k4 are constants. I cannot express the system as:
y1'' = (y1,y1',y2,y2')
y2'' = (y1,y1',y2,y2')
because the system of equations is transcendental.
How can I solve the differencial equation system? I don't need the algebraic solution, but a numerical solution given an initial value.
Thanks

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