I am trying to solve the following system of two coupled partial differential equations (both equations equal 0):

Here, $V$ and $Y$ are functions that only depend on $r$, i.e., $V=V(r)$ and $Y=Y(r)$. $alpha$, $beta$, $gamma$ and $k^{-2}$ are just constants, $H^{Lmu}_mu=0$ and $H^{Li}_i-H^{Lt}_t=0$. I’ve tried to use DSolve but it doesn’t work:

```
DSolve({2*(3*b - a))*1/r^4*(r^2*v'(r))'' - ck*1/r^2*(r^2*v'(r))' - 4*(3*b - a)*1/r^2*(r^2*Y'(r))' + 2*ckY(r) == 0, 2*b*1/r^4*(r^2*v'(r))'' - ck*1/r^2*(r^2*v'(r))' + 2*(a - 2*b)*1/r^2*(r^2*Y'(r))' == 0}, {v, Y}, r)
```

I don’t know much about mathematica and this problem is untractable without numerical methods. Can someone send some help? Thank you so much.