After some private conversations, it turns out that x(t) is a sinusoidal function and y(t) is it's first derivative.
To be fit is the function z(t)=(a+b*x+c*x^2+d*x^3+e*x^4)*y+A*x*exp(B*x)
I have quickly implemented the above ideas and made a demo VI using simulated data with noise. It converges very fast from all zero parameters estimates and seems very stable. I am sure many improvements are possible.