# NDSolve initial value not explicitly specified

I'm trying to solve for 2 first order coupled ODEs. I've got two initial conditions, and I can't get a solution. I've double checked my equation input and my initial conditions, and my NDSolve function looks similar to the example posted in the documentation so I'm stumped. Here's what I've got going:

gamma := 0;
Ra := 2.32 * 10^9;
Ja :=  0.315;
C1 :=  .5;
C2 := .6666;
qdotc := 1;
C3 := .75;

sol = NDSolve[
{delta'[t] ==
C1 * Ja * (1 + gamma * delta[t]) / (delta[t]^3 * Ra * Sin[t]) -
C2 * (delta[t]) * Cot[t],
q'[t] == 1/ delta[t] * Sin[t],
delta[0] == 0.00317666163538945,
q[0] == 0
},
{delta, q},
{t, 0, 1},
Method -> {"StiffnessSwitching",
Method -> {"ExplicitRungeKutta", Automatic}},
WorkingPrecision -> 100][[1, 1]]

Plot[Evaluate[delta[t] /. sol], {t, 0, 1}, PlotRange -> All]


And then I get the following error messages:

• Your ode -system is of order 1 , though your initial condition q'[0]== 0 isn't allowed! – Ulrich Neumann Nov 13 '18 at 8:09
• The precision issue is because you are using approximate numbers, and then trying to specify WorkingPrecision to be 100. The second error is because $cot(0)$ is a divide by zero error. – KraZug Nov 13 '18 at 8:36

gamma = 0;
Ra = 232*10^7;
Ja = 315/1000;
C1 = 1/2;
C2 = 6666/10000;
qdotc = 1;
C3 = 75/100;
t0 = 10^-5;
q0 = Rationalize[0.00317666163538945];
sol = NDSolve[{delta'[t] ==
C1*Ja*(1 + gamma*delta[t])/(delta[t]^3*Ra*Sin[t]) -
C2*(delta[t])*Cot[t], q'[t] == 1/delta[t]*Sin[t],
delta[t0] == q0, q[t0] == 0}, {delta, q}, {t, t0, 1}]

Plot[Evaluate[delta[t] /. First[sol]], {t, t0, 1}, PlotRange -> All]


• Thank you! Works perfectly now. – Drew Lilley Nov 13 '18 at 18:39
• You're welcome! – Alex Trounev Nov 13 '18 at 19:45