ODE
\[ \text {f1} y'(x) y''(x)+\text {f2} y(x) y''(x)+\text {f3} y'(x)^2+\text {f4} y(x) y'(x)+\text {f5} y(x)^2=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.287738 (sec), leaf count = 0 , could not solve
DSolve[f5*y[x]^2 + f4*y[x]*Derivative[1][y][x] + f3*Derivative[1][y][x]^2 + f2*y[x]*Derivative[2][y][x] + f1*Derivative[1][y][x]*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.112 (sec), leaf count = 50
\[ \left \{ \ln \left ( y \left ( x \right ) \right ) -\int \!{\it RootOf} \left ( x+\int ^{{\it \_Z}}\!{\frac {{\it \_f}\,{\it f1}+{\it f2}}{{{\it \_f}}^{3}{\it f1}+{{\it \_f}}^{2}{\it f2}+{{\it \_f}}^{2}{\it f3}+{\it \_f}\,{\it f4}+{\it f5}}}{d{\it \_f}}+{\it \_C1} \right ) \,{\rm d}x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[f5*y[x]^2 + f4*y[x]*y'[x] + f3*y'[x]^2 + f2*y[x]*y''[x] + f1*y'[x]*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[f5*y[x]^2 + f4*y[x]*Derivative[1][y][x] + f3*Derivative[1][y][x]^2 + f2*y[x]*Derivative[2][y][x] + f1*Derivative[1][y][x]*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(f1*diff(y(x),x)*diff(diff(y(x),x),x)+f2*y(x)*diff(diff(y(x),x),x)+f3*diff(y(x),x)^2+f4*y(x)*diff(y(x),x)+f5*y(x)^2 = 0, y(x),'implicit')
Maple raw output
ln(y(x))-Int(RootOf(x+Intat(1/(_f^3*f1+_f^2*f2+_f^2*f3+_f*f4+f5)*(_f*f1+f2),_f = _Z)+_C1),x)-_C2 = 0