4.38.28 \(x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0\)

ODE
\[ x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✗
cpu = 22.4883 (sec), leaf count = 0 , could not solve

DSolve[24 + 12*x*y[x] + x^3*(-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x]) == 0, y[x], x]

Maple ✓
cpu = 0.931 (sec), leaf count = 94

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =- \left ( \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}-14\,{\it \_a}-24 \right ) {\it \_b} \left ( {\it \_a} \right ) +{\it \_a}-3 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}=xy \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) =-{\frac {1}{x \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) \right ) }} \right \} , \left \{ x= \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{-1},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \] Mathematica raw input

DSolve[24 + 12*x*y[x] + x^3*(-y[x]^3 + y[x]*y'[x] + y''[x]) == 0,y[x],x]

Mathematica raw output

DSolve[24 + 12*x*y[x] + x^3*(-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][
y][x]) == 0, y[x], x]

Maple raw input

dsolve(x^3*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)+12*x*y(x)+24 = 0, y(x),'implicit')

Maple raw output

y(x) = ODESolStruc(_a*exp(Int(_b(_a),_a)+_C1),[{diff(_b(_a),_a) = -((_a^3+_a^2-1
4*_a-24)*_b(_a)+_a-3)*_b(_a)^2}, {_a = x*y(x), _b(_a) = -1/x/(x*diff(y(x),x)+y(x
))}, {x = 1/exp(Int(_b(_a),_a)+_C1), y(x) = _a*exp(Int(_b(_a),_a)+_C1)}])