4.22.34 \(y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\)

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

[[_1st_order, _with_linear_symmetries]]

Book solution method
Change of variable

Mathematica
cpu = 600.116 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.597 (sec), leaf count = 38

\[ \left \{ \left ( y \left ( x \right ) \right ) ^{4}+{\frac {32\,{x}^{3}}{27}}=0,[x \left ( {\it \_T} \right ) =-{\frac { \left ( {\it \_C1}\,{{\it \_T}}^{2}-1 \right ) {\it \_C1}}{2\,{{\it \_T}}^{2}}},y \left ( {\it \_T} \right ) ={\frac {{\it \_C1}}{{\it \_T}}}] \right \} \] Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

y(x)^4+32/27*x^3 = 0, [x(_T) = -1/2*(_C1*_T^2-1)/_T^2*_C1, y(_T) = 1/_T*_C1]