I have the following DAE system of equations

```
(Rho)0 = 1;
M = 1;
eq1 = D(m(t, r), r) - 4 Pi (Rho)(t, r) R(t, r)^2 D(R(t, r), r);
eq2 = D(m(t, r), t) + (4 Pi)/3 (Rho)(t, r) R(t, r)^2 D(R(t, r), t);
eq3 = D(R(t, r), r, t) - D(R(t, r), t) D((Nu)(t, r), r) -
D(R(t, r), r) D((Lambda)(t, r), t);
eq4 = D((Rho)(t, r), r) + 1/4 (Rho)(t, r) D((Nu)(t, r), r);
eq5 = Exp(-2 (Nu)(t, r)) (D(R(t, r), {t, 2}) -
D((Nu)(t, r), t) D(R(t, r), t)) -
Exp(-2 (Lambda)(t, r)) D((Nu)(t, r), r) D(R(t, r), r) + m(t, r)/
R(t, r)^2 + (4 Pi)/3 (Rho)(t, r) R(t, r);
```

I have some problem finding initial conditions that produce solutions: how can I vary the initial conditions to see when the system has solutions? Currently I am just trying different random values, but it is obviously not the best method. I use `NDSolveValue`

as follows:

```
NDSolveValue({eq1 == 0, eq2 == 0, eq3 == 0, eq4 == 0,
eq5 == 0, (Rho)(0, r) == (Rho)0, (Rho)(t, 0) == (Rho)0,
m(0, r) == M,
m(t, 0) ==
M, (Nu)(0, r) == -(1/4) Log((Rho)0), (Nu)(t,
0) == -(1/4) Log((Rho)0), (Lambda)(0, r) ==
0, (Lambda)(t, 0) == 0, R(0, r) == ((3 M)/(4 Pi (Rho)0))^(1/3),
R(t, 0) == ((3 M)/(4 Pi (Rho)0))^(1/3),
Derivative(1, 0)(R)(0, r) == 1}, {(Rho), R,
m, (Nu), (Lambda)}, {t, 0, 1}, {r, 0, 1})
```