How to solve a transcendental differential equation?

Question

回答： Rohit Pappu 2021-3-16

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

Answer 1

Rohit Pappu 2021-3-16

Please refer to this community answer