4.41.29 \(x^3 y(x)^2 y''(x)+(y(x)+x) \left (x y'(x)-y(x)\right )^3=0\)

ODE
\[ x^3 y(x)^2 y''(x)+(y(x)+x) \left (x y'(x)-y(x)\right )^3=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✗
cpu = 38.0563 (sec), leaf count = 0 , could not solve

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

Maple ✓
cpu = 0.235 (sec), leaf count = 131

\[ \left \{ \ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{2\,{\it \_f}} \left ( 2\,\sqrt {{\it \_f}}{{\sl J}_{i\sqrt {3}+1}\left (2\,\sqrt {{\it \_f}}\right )}+2\,\sqrt {{\it \_f}}{\it \_C1}\,{{\sl Y}_{i\sqrt {3}+1}\left (2\,\sqrt {{\it \_f}}\right )}- \left ( i\sqrt {3}+1 \right ) \left ( {{\sl Y}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}{\it \_C1}+{{\sl J}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )} \right ) \right ) \left ( {{\sl Y}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}{\it \_C1}+{{\sl J}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )} \right ) ^{-1}}{d{\it \_f}}-{\it \_C2}=0 \right \} \] Mathematica raw input

DSolve[(x + y[x])*(-y[x] + x*y'[x])^3 + x^3*y[x]^2*y''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x^3*y(x)^2*diff(diff(y(x),x),x)+(x+y(x))*(x*diff(y(x),x)-y(x))^3 = 0, y(x),'implicit')

Maple raw output

ln(x)-Intat(1/2*(2*_f^(1/2)*BesselJ(I*3^(1/2)+1,2*_f^(1/2))+2*_f^(1/2)*_C1*Besse
lY(I*3^(1/2)+1,2*_f^(1/2))-(I*3^(1/2)+1)*(BesselY(I*3^(1/2),2*_f^(1/2))*_C1+Bess
elJ(I*3^(1/2),2*_f^(1/2))))/_f/(BesselY(I*3^(1/2),2*_f^(1/2))*_C1+BesselJ(I*3^(1
/2),2*_f^(1/2))),_f = y(x)/x)-_C2 = 0