Hi, I'm having some trouble with this problem...if anyone could help me out a bit that'd be great - it's really just one bit of it i don't get.
Solve the pair of differential equations:
dx/dt = ax dy/dt = ay + bx
where a and b are arbitrary constants. All subject to the initial conditions x(0)=2 , y(0) = 1.
So basically I converted it to a 2nd order ODE (d2y/dx2= ...) as this is the only method i've been taught, and found the general solution - all seemed to be ok up until then. The general solution was, i think, of the form y = A exp(at) + Bt exp(at). (Where A and B are constants)
From there, i can plug the y(0) condition in, and get an expression which tells me A is 1. But i've no idea how to use the x(0) initial condition, or indeed what it really means (x at t=0?), and i'm pretty certain i need to do so in order to find both A and B...
Any advice would be hugely appreciated! Thanks.