Nonlinear ODE: Analytical Solution?

[Pepo]

Nonlinear 1st order ODE

$$\frac{dH}{dt}$$=B-A*(H-Z)$$^{3/2}$$
where:
B,A and Z are known values

H=f(t); H is function of t




I've already solve this ODE numerically using a 4th order RK routine. But my question is, it is possible to get an analytical solution for H(t)?

 

[lanedance]

first let h = H-Z, then you get

h' = b-ah^(3/2)

 

[lanedance]

mathematica finds it messy...
http://www.wolframalpha.com/input/?i=h'(t)+%3D+b-a*(h(t))^(3/2)

 

[Pepo]

first let h = H-Z, then you get

h' = b-ah^(3/2)

mathematica finds it messy...
http://www.wolframalpha.com/input/?i=h'(t)+%3D+b-a*(h(t))^(3/2)

I have try it plugging it with h=H-Z in mathematica but the solution is a mess. I really don't know how to get an expression for H(t) from this. :-/

 

[lanedance]

there may not be one...