I've been working on my master thesis and faced with a big problem. I don't know how to formulate this problem in mathematica.
I'm working with modified TOV on Jordan Frame and i have three equations to solve

$\phi[r]= 2\alpha R[r]+1$

$\lambda'= \frac{1}{\left(2r\phi+\phi'r^{2}\right)}\left\{ \exp\left(2\lambda\right)\left[k\rho r^{2}-\frac{1}{8\alpha}\left(\phi-1\right)^{2}r^{2}-\phi\right]+\phi+2r\phi'\left(r\nu'+1\right)+\phi''r^{2}\right\}$

$\nu'= \frac{1}{\left(2r\phi+\phi'r^{2}\right)}\left\{ \exp\left(2\lambda\right)\left[kPr^{2}+\frac{1}{8\alpha}\left(\phi-1\right)^{2}r^{2}+\phi\right]+2\lambda'\phi'-2\phi'r-\phi\right\}$

where $\lambda, \nu, \phi$ are function of r.

I have three conditions
$\nu[0] =0 \\ \lambda[0] =0\\ \phi[0]>0$

how can I fix my problem?

Suppose that the EoS is $P[r] = k * rho[r] ^2$