ODE
\[ -2 y'''(x)+y''''(x)+y(x)^2=0 \] ODE Classification
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.024828 (sec), leaf count = 0 , could not solve
DSolve[y[x]^2 - 2*Derivative[3][y][x] + Derivative[4][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.904 (sec), leaf count = 91
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {{\rm d}^{3}}{{\rm d}{{\it \_a}}^{3}}}{\it \_b} \left ( {\it \_a} \right ) \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}+4\, \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) -1/2 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{{\it \_a}}^{2}}}{\it \_b} \left ( {\it \_a} \right ) + \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}{\it \_b} \left ( {\it \_a} \right ) -2\, \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}{\it \_b} \left ( {\it \_a} \right ) +{{\it \_a}}^{2}=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[y[x]^2 - 2*y'''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
DSolve[y[x]^2 - 2*Derivative[3][y][x] + Derivative[4][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(diff(y(x),x),x),x)+y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a,[{diff(diff(diff(_b(_a),_a),_a),_a)*_b(_a)^3+4*(diff(_b(_a),_a)-1/2)*_b(_a)^2*diff(diff(_b(_a),_a),_a)+diff(_b(_a),_a)^3*_b(_a)-2*diff(_b(_a),_a)^2*_b(_a)+_a^2 = 0}, {_a = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a),_a)+_C1, y(x) = _a}])