OK. Sorry for the missunderstanding.
May be, you could use an algorithm of this kind:
Start with given initial values y and t.
Recursive process :
Compute A(y,t), B(y,t), C(y,t) and D(y,t)
Solve X=A+B+f(C,D,X) with a numerical equation solver, introduced as sub-program.
With the computed value X=dy/dt the incrementation of y is done, as well as the incrementation of t.
Then continue the recursive process.