##### 4.18.23 $$9 x^2+x y'(x)^2-3 y(x) y'(x)=0$$

ODE
$9 x^2+x y'(x)^2-3 y(x) y'(x)=0$ ODE Classiﬁcation

[[_homogeneous, class G]]

Book solution method
No Missing Variables ODE, Solve for $$y$$

Mathematica
cpu = 0.637147 (sec), leaf count = 59

$\left \{\left \{y(x)\to -\frac {2 x^{3/2}}{\sqrt {\text {sech}^2\left (\frac {3}{2} (-\log (x)+c_1)\right )}}\right \},\left \{y(x)\to \frac {2 x^{3/2}}{\sqrt {\text {sech}^2\left (\frac {3}{2} (-\log (x)+c_1)\right )}}\right \}\right \}$

Maple
cpu = 1.738 (sec), leaf count = 51

$\left [y \left (x \right ) = -2 x^{\frac {3}{2}}, y \left (x \right ) = 2 x^{\frac {3}{2}}, y \left (x \right ) = \frac {4 x^{3}+\textit {\_C1}^{2}}{2 \textit {\_C1}}, y \left (x \right ) = \frac {\textit {\_C1}^{2} x^{3}+4}{2 \textit {\_C1}}\right ]$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> (-2*x^(3/2))/Sqrt[Sech[(3*(C[1] - Log[x]))/2]^2]}, {y[x] -> (2*x^(3/2)
)/Sqrt[Sech[(3*(C[1] - Log[x]))/2]^2]}}

Maple raw input

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

Maple raw output

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