How Can I solve this System of ODE ? $$ \frac{dy}{dx}=a(x)y+b(x)u $$ $$ \frac{du}{dx}=c(x)y+d(x)u $$
I can solve this system with constant coefficient but, I wonder if there is any relation between the method of solving system of ODE with constant coefficient and with variable coefficient ? and Is the method of solving for system with constant coefficient special case of the method of solving for system with variable coefficient or not ?
Thank you ...
There are no general methods for solving linear systems (or equations) of ODE's with variable coefficients. If you know one solution, you can reduce the order of the system by the method of Reduction of order. Under certain analyticity conditions on the coefficients, you may be able to find power series solutions.