I desperately need to solve a coupled system of linear second order differential equations of the form:
$ a_1x''+ b_1x' + c_1y'' + d_1y' =0 $
$ a_2x'' + b_2x' + c_2y'' + d_2y' + e_2y = 0 $
initial conditions are :
$ y(0)=y_0, y'(0)=x(0)=x'(0)=0. $
x and y are displacement in time.
What method do you suggest for solving this system? Any suggestion will be appreciated!
Thanks!
Best Answer
In case of linear ODE with constant coefficients, it is known that the general solution is a linear combination of exponential functions on the form $k\,e^{r\,t}$ where the various values of $r$ , real or complex, are the roots of a polynomial equation. So, a method to solve the system is to presume of the form of particular solutions and determine the parameters of them, as done below :