Thread Subject: Third order differential equation

Hi,

I need to know how to solve the following equation via matlab:

f.f'''+k.f'.f''=0

where f is a function of x: f(x)
and k is a constant

Can it even be solved at all?

Regards,

Uchiha Sama

> Hi,
>
> I need to know how to solve the following equation
> via matlab:
>
> f.f'''+k.f'.f''=0
>
> where f is a function of x: f(x)
> and k is a constant
>
> Can it even be solved at all?
>
> Regards,
>
> Uchiha Sama

Divide your equation by f'*f''' to get
log(f(t)/f(t0)) = -k*log(f''(t)/f''(t0))
or
f(t)/f(t0) = (f''(t)/f''(t0))^(-k)
or
f(t)*f''(t0)^(-k) - f''(t)^(-k)*f(t0) = 0.
Now setting f = y, f'=z gives the system
y' = z
z' = (y*f''(t0)^(-k)/f(t0))^(-1/k)
which can be solved easily using one of the solvers
of the ODE suite.

Best wishes
Torsten.