ODE
\[ f\left (x,y'(x),y''(x)\right )=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✗
cpu = 1.32168 (sec), leaf count = 0 , could not solve
DSolve[f[x, Derivative[1][y][x], Derivative[2][y][x]] == 0, y[x], x]
Maple ✓
cpu = 0.132 (sec), leaf count = 48
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\it RootOf} \left ( f \left ( {\it \_a},{\it \_b} \left ( {\it \_a} \right ) ,{\it \_Z} \right ) \right ) \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) =\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[f[x, y'[x], y''[x]] == 0,y[x],x]
Mathematica raw output
DSolve[f[x, Derivative[1][y][x], Derivative[2][y][x]] == 0, y[x], x]
Maple raw input
dsolve(f(x,diff(y(x),x),diff(diff(y(x),x),x)) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(Int(_b(_a),_a)+_C1,[{diff(_b(_a),_a) = RootOf(f(_a,_b(_a),_Z))}, {_a = x, _b(_a) = diff(y(x),x)}, {x = _a, y(x) = Int(_b(_a),_a)+_C1}])