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 = 1.14602 (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 = 2.103 (sec), leaf count = 45
\[\left [y \left (x \right ) = {\mathrm e}^{\int \RootOf \left (x +\int _{}^{\textit {\_Z}}\frac {\textit {\_f} \mathit {f1} +\mathit {f2}}{\textit {\_f}^{3} \mathit {f1} +\textit {\_f}^{2} \mathit {f2} +\textit {\_f}^{2} \mathit {f3} +\textit {\_f} \mathit {f4} +\mathit {f5}}d \textit {\_f} +\textit {\_C1} \right )d x +\textit {\_C2}}\right ]\] 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))
Maple raw output
[y(x) = exp(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)]