tumor growth

[ninaricci]

can any one show me how to solve this equation that represents the tumor growth
ds/dt = - a s ln(bs)
where a and b are constants

[Tide]

First, change variable to u = bs which gives

\frac {du}{dt} = -a u \ln u

which you can integrate by setting

\frac {du}{u \ln u} = -a dt

so that

\ln \frac {\ln u}{\ln u_0} = -a t

where u_0 is the initial condition. You can exponentiate both sides twice to obtain an explicit solution for u(t) and finally s(t).