\[ y''(x)-\frac {1}{\left (a y(x)^2+b x y(x)+c x^2+d y(x)+e x+k\right )^{3/2}}=0 \] ✗ Mathematica : cpu = 60.4097 (sec), leaf count = 0
DSolve[-(k + e*x + c*x^2 + d*y[x] + b*x*y[x] + a*y[x]^2)^(-3/2) + Derivative[2][y][x] == 0,y[x],x]
, could not solve
DSolve[-(k + e*x + c*x^2 + d*y[x] + b*x*y[x] + a*y[x]^2)^(-3/2) + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 42.077 (sec), leaf count = 8413
dsolve(diff(diff(y(x),x),x)-1/(a*y(x)^2+b*x*y(x)+c*x^2+alpha*y(x)+beta*x+gamma)^(3/2)=0,y(x))
\[\text {Expression too large to display}\]