How could be solved (either numerically or analytically) the following dynamic system?
$$\frac{dv}{dt}=a(\frac{h+b.v^2}{h+b.v^2+c})$$ $$\frac{dh}{dt}=d-f.t-g.v$$
where: a, b,c,d,f and g are positive scalars. Boundary conditions: $v(0)=v_0$ and $h(0)=0$
This system is an preliminary model for my undergrade engineering thesis project which is about pulsatile flowes. Finally, i suppose that function solution will contain an exponential form.
Regards,