How to solve a first and second order coupled differential equations

Hi, I need to solve a coupled differential equations to model a modification of the Drude-Lorentz model. One of these equations is a first order, the other one a second order equation.

(dx/dt)+(x/a)=ay

(d^2y/dt^2)+(1/b)*dy/dt+cy/d=e*x

Where a, b, c, d, e are constants and x, y the wanted results.

I can't find the way to make it the easiest possible, any idea? Thanks

Answer 1

[Andrei Bobrov]

Try this is code with use Symbolic Toolbox:

syms a b c d e x(t) y(t)
z = dsolve(diff(x) + x/a == a*y,diff(y,2) + 1/b*diff(y) + c*y/d == e*x)