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

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

[[_1st_order, _with_linear_symmetries]]

Book solution method
Change of variable

Mathematica
cpu = 599.997 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.231 (sec), leaf count = 65

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

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

y(x)^2+1/4*x^4 = 0, -_C1+x^2+(x^4+4*y(x)^2)^(1/2) = 0, -_C1+1/y(x)^2*x^2+1/y(x)^
2*(x^4+4*y(x)^2)^(1/2) = 0