ODE
\[ f\left (y(x),y'(x),y''(x)\right )=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 6.29472 (sec), leaf count = 0 , could not solve
DSolve[f[y[x], Derivative[1][y][x], Derivative[2][y][x]] == 0, y[x], x]
Maple ✓
cpu = 0.152 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) -{\it RootOf} \left ( f \left ( {\it \_a},{\it \_b} \left ( {\it \_a} \right ) ,{\it \_Z} \right ) \right ) =0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[f[y[x], y'[x], y''[x]] == 0,y[x],x]
Mathematica raw output
DSolve[f[y[x], Derivative[1][y][x], Derivative[2][y][x]] == 0, y[x], x]
Maple raw input
dsolve(f(y(x),diff(y(x),x),diff(diff(y(x),x),x)) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a,[{diff(_b(_a),_a)*_b(_a)-RootOf(f(_a,_b(_a),_Z)) = 0}, {_a = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a),_a)+_C1, y(x) = _a}])