How does MATLAB's ode45 handle highly coupled ODEs (where y' depends on x' and x' depends on y', etc.)? -

if have 2 sets of highly coupled odes such as:

dy/dt = a*dx/dt + b*y + c*x dx/dt = d*dy/dt + e*y + f*x

or if have system like:

u = function(dy/dt) dy/dt = function(u,...)

how ode45 handle this? if following:

dy(1) = a*dy(2) + b*y(1) + c*y(2) dy(2) = d*dy(1) + e*y(1) + f*y(2)

or second problem:

u = a*dy(1) + ... dy(1) = b*u + ...

and run ode45, matlab produces results without complaint i'm hesitant i'm not sure how it's handling such coupled system of equations. , suggestions?

Three