# Solving second order non-linear DE with boundary condition

I was trying to get some result from this equation but I can't find the solution. please see what is wrong with it??!! thanks

f, s are positive and k will be negative or positive.

    Clear["Global*"]
eqn = {(y''[x]/y[x]) + s (y'[x]/y[x])^2 - s (k/y[x]^2) - f/2 == 0};
k = 3; f = 7/10; s = 1/2;
sol = DSolve[{eqn, y[0] == 1, y'[0] == 1}, y, x]

• nothing wrong with it. Mathematica can't solve it. Here is Maple's solution $y \left(x \right) = \mathit{RootOf}\left(-\left(\int_{\textit{\_b}}^{\textit{\_Z}}\frac{\textit{\_a} \sqrt{30}}{\sqrt{\textit{\_a} \left(7 \textit{\_a}^{3}+30 \mathit{RootOf}\left(-\sqrt{30}+\sqrt{97+30 \textit{\_Z}}\right)+90 \textit{\_a} \right)}}d \textit{\_a} \right)+x +\int_{\textit{\_b}}^{1}\frac{\textit{\_a} \sqrt{30}}{\sqrt{\textit{\_a} \left(7 \textit{\_a}^{3}+30 \mathit{RootOf}\left(-\sqrt{30}+\sqrt{97+30 \textit{\_Z}}\right)+90 \textit{\_a} \right)}}d \textit{\_a} \right)$ Jun 13 at 19:58
• @Nasser: I'm not familiar with Maple syntax, but does that answer include the boundary conditions? I ask because Mathematica does return an answer if the boundary conditions are removed from the DSolve (It returns an ugly object in terms of Solve and Root and EllipticF, but I suspect it's effectively the same as Maple's solution in the general case.) Jun 13 at 20:27
• @MichaelSeifert Yes, the above answer includes the BC. Here is screen shot. !Mathematica graphics Jun 13 at 20:41
• Because the Maple solution is of little value unless evaluated numerically, eqn may as well be solved numerically with NDSolveValue[{eqn, y[0] == 1, y'[0] == 1}, y[x], {x, -6, 5}]`. I did make some progress with the symbolic solution but ultimately had to invert it numerically. Jun 14 at 5:02