##### 4.19.42 $$4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0$$

ODE
$4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0$ ODE Classiﬁcation

[[_homogeneous, class G]]

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

Mathematica
cpu = 1.02101 (sec), leaf count = 121

$\left \{\text {Solve}\left [\log (x)=\frac {2 x^{5/2} \sqrt {1-x^3 y(x)^2} \sin ^{-1}\left (x^{3/2} y(x)\right )}{3 \sqrt {x^5 \left (x^3 y(x)^2-1\right )}}+c_1,y(x)\right ],\text {Solve}\left [\frac {2 x^{5/2} \sqrt {1-x^3 y(x)^2} \sin ^{-1}\left (x^{3/2} y(x)\right )}{3 \sqrt {x^5 \left (x^3 y(x)^2-1\right )}}+\log (x)=c_1,y(x)\right ]\right \}$

Maple
cpu = 2.741 (sec), leaf count = 53

$\left [y \left (x \right ) = \frac {1}{x^{\frac {3}{2}}}, y \left (x \right ) = -\frac {1}{x^{\frac {3}{2}}}, y \left (x \right ) = \frac {\textit {\_C1}^{2} x^{3}+1}{2 \textit {\_C1} \,x^{3}}, y \left (x \right ) = \frac {x^{3}+\textit {\_C1}^{2}}{2 \textit {\_C1} \,x^{3}}\right ]$ Mathematica raw input

DSolve[9 + 12*x^4*y[x]*y'[x] + 4*x^5*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{Solve[Log[x] == C[1] + (2*x^(5/2)*ArcSin[x^(3/2)*y[x]]*Sqrt[1 - x^3*y[x]^2])/(3
*Sqrt[x^5*(-1 + x^3*y[x]^2)]), y[x]], Solve[Log[x] + (2*x^(5/2)*ArcSin[x^(3/2)*y
[x]]*Sqrt[1 - x^3*y[x]^2])/(3*Sqrt[x^5*(-1 + x^3*y[x]^2)]) == C[1], y[x]]}

Maple raw input

dsolve(4*x^5*diff(y(x),x)^2+12*x^4*y(x)*diff(y(x),x)+9 = 0, y(x))

Maple raw output

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