The code provided has a few issues and can be refined to ensure it runs correctly in Mathematica. Here's a corrected version of the code:
(*Define the differential equation*)
eqn = (s''[x]/
s[x]) + ((3 \[Gamma])/2 - 1) (s'[x]/s[x])^2 - (3 \[Gamma]*f)/
2 == 0;
(*Solve the differential equation numerically with specified \
parameters*)
sol = NDSolveValue[{eqn /. {f -> 0.7, \[Gamma] -> 1}, s'[1] == 1,
s[1] == 1}, s, {x, 0.1, 8}];
(*Plot the numerical solution*)
pp1 = Plot[Evaluate[sol[x]], {x, 0.1, 8},
PlotStyle -> {Opacity[.2], AbsoluteThickness[5]}];
(*Solve the differential equation symbolically*)
sol1 = DSolve[{(w''[t]/
w[t]) + ((3 \[Gamma])/2 - 1) (w'[t]/w[t])^2 - (3 \[Gamma]*p)/
2 == 0, w'[1] == 1, w[1] == 1}, w[t], t];
(*Set parameters*)
p = 0.7; \[Gamma] = 1;
(*Plot the symbolic solution*)
pp2 = Plot[Evaluate[w[t] /. sol1], {t, 0.1, 8},
PlotStyle -> {Dashed, Red}];
(*Show both plots together*)
Show[pp1, pp2]
It took 15 minutes and it gave me the following plot