\[ a+f(x) y(x)^2+2 y(x) y''(x)-y'(x)^2=0 \] ✗ Mathematica : cpu = 0.0239998 (sec), leaf count = 0 , could not solve
DSolve[a + f[x]*y[x]^2 - Derivative[1][y][x]^2 + 2*y[x]*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+f(x)*y(x)^2+a=0,y(x))