4.20.11 \(4 x^3 y'(x)-4 x^2 y(x)+9 y(x) y'(x)^2=0\)

ODE
\[ 4 x^3 y'(x)-4 x^2 y(x)+9 y(x) y'(x)^2=0 \] 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 = 0.239 (sec), leaf count = 65

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+{\frac {{x}^{4}}{9}}=0,-{\it \_C1}+{x}^{2}+\sqrt {{x}^{4}+9\, \left (y \relax (x ) \right ) ^{2}}=0,-{\it \_C1}+{\frac {{x}^{2}}{ \left (y \relax (x ) \right ) ^{2}}}+{\frac {1}{ \left (y \relax (x ) \right ) ^{2}}\sqrt {{x}^{4}+9\, \left (y \relax (x ) \right ) ^{2}}}=0 \right \} \] Mathematica raw input

DSolve[-4*x^2*y[x] + 4*x^3*y'[x] + 9*y[x]*y'[x]^2 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(9*y(x)*diff(y(x),x)^2+4*x^3*diff(y(x),x)-4*x^2*y(x) = 0, y(x),'implicit')

Maple raw output

y(x)^2+1/9*x^4 = 0, -_C1+1/y(x)^2*x^2+1/y(x)^2*(x^4+9*y(x)^2)^(1/2) = 0, -_C1+x^
2+(x^4+9*y(x)^2)^(1/2) = 0