# Tumor growth

1. Oct 11, 2004

### 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

Last edited: Oct 11, 2004
2. Oct 11, 2004

### 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).