The set od equations you are trying to solve COUPLED set of ODEs. It is actually very easy to do in matlab using ODE45. You need the initial conditions of all the y's in your equation. I believe you know some linear algebra. Take Y=[y1 y2 y3] as the vector you want to find. Let Y0=[y10 y20 y30] be the IC(you should put the values of y10 y20 y30). Define the range of independant variable for which you need the solution. x=xmin:xmax; call [xout,Yout]=ode45(@yourfxn,x,Y0); xout is the range of independant variable numerically used. First column of Y is y1 and so on; define yourfxn as a function. function Y'=yourfxn(x,Y); define what is your function doing. Y'=AY, where A is the coeffienct matrix.
Hope this helps!!!! Lot of solutions and examples can be found online for this
