# How do I solve this ODE numerically in Mathematica?

I want to solve these equations numerically in Mathematica and plot them.

$$u'(t)=1.5\,u(t)\,v(t)-u(t) \space \space \space \text{and} \space \space u(0)=0.001$$ $$v'(t)=-1.5\,u(t)\,v(t) \space \space \space \text{and} \space \space v(0)=0.999$$ $$z'(t)=u(t) \space \space \space \text{and} \space \space z(0)=0$$

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.

• Clear all the variables you used, and try again with the change z[0] == 0. Note the difference between equality (==) and assignment (=). – J. M. is in limbo Jun 17 '15 at 13:17
• Still doesn't work. I get this: NDSolve::deqn: "Equation or list of equations expected instead of True in the first argument {\!(True, *SuperscriptBox[\"u\", \"[Prime]\", MultilineFunction->None][t] == (-5)\\\ u[t]\\\ v[t], True, 0.001` == u[0] == 0 == 0)}." – Trix Jun 17 '15 at 13:19
• I said, clear everything. Start in a fresh session if need be. The error you showed tells me you didn't do the first thing I told you to do. – J. M. is in limbo Jun 17 '15 at 13:22
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This is mostly because your code is completely unrelated to your equation.

• What is w?
• Why do you use = when you want ==?
• Where does the 5 come from when you want 1.5?
• Why are all of your initial values 0?

Here is something to start with but first go to Evaluation -> Quit Kernel

sol = NDSolveValue[{
u'[t] == 1.5 u[t] v[t] - u[t],
v'[t] == -1.5 u[t] v[t],
z'[t] == u[t],
u[0] == 0.001,
v[0] == 0.999,
z[0] == 0}, {u, v, z}, {t, 10}]

Plot[Through[sol[t]], {t, 0, 10}, PlotRange -> All, Evaluated -> True]

• It works now. Thanks! – Trix Jun 17 '15 at 13:25
• @Trix If this answer is the solution, then mark it with the green checkmark that you find below the up- and downvote buttons. – halirutan Jun 17 '15 at 13:26
• @BobHanlon Fixed it. Thanks. – halirutan Jun 17 '15 at 14:53