ODE
\[ \text {f0}(y(x)) y''(x)+\text {f1}(y(x)) y'(x)^2+\text {f2}(y(x)) y'(x)+\text {f3}(y(x))=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 101.26 (sec), leaf count = 0 , could not solve
DSolve[f3[y[x]] + f2[y[x]]*Derivative[1][y][x] + f1[y[x]]*Derivative[1][y][x]^2 + f0[y[x]]*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 1.207 (sec), leaf count = 65
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +{\frac {{\it f1} \left ( {\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\it f2} \left ( {\it \_a} \right ) {\it \_b} \left ( {\it \_a} \right ) +{\it f3} \left ( {\it \_a} \right ) }{{\it f0} \left ( {\it \_a} \right ) }}=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[f3[y[x]] + f2[y[x]]*y'[x] + f1[y[x]]*y'[x]^2 + f0[y[x]]*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[f3[y[x]] + f2[y[x]]*Derivative[1][y][x] + f1[y[x]]*Derivative[1][y][x]^2 + f0[y[x]]*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(f0(y(x))*diff(diff(y(x),x),x)+f1(y(x))*diff(y(x),x)^2+f2(y(x))*diff(y(x),x)+f3(y(x)) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a,[{diff(_b(_a),_a)*_b(_a)+(f1(_a)*_b(_a)^2+f2(_a)*_b(_a)+f3(_a))/f0(_a) = 0}, {_a = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a),_a)+_C1, y(x) = _a}])