I want to solve these equations numerically in Mathematica and plot them.
\begin{equation} u'(t)=1.5\,u(t)\,v(t)-u(t) \space \space \space \text{and} \space \space u(0)=0.001 \end{equation} \begin{equation} v'(t)=-1.5\,u(t)\,v(t) \space \space \space \text{and} \space \space v(0)=0.999 \end{equation} \begin{equation} z'(t)=u(t) \space \space \space \text{and} \space \space z(0)=0 \end{equation}
I have tried this:
sol = NDSolve[{u'[t] == -u[t] + 1.5 u[t] v[t],
v'[t] == 1.5 u[t] v[t], w'[t] = u[t],
u[0] == v[0] == z[0] = 0},
{u, v, w}, {t, 10}]
But it doesn't seem to work. Thanks in advance.

z[0] == 0. Note the difference between equality (==) and assignment (=). – J. M.'s missing motivation Jun 17 '15 at 13:17{}button above the edit window. The edit window help button?is also useful for learning how to format your questions and answers. – Michael E2 Jun 17 '15 at 13:46