##### 4.18.35 $$3 x y'(x)^2-6 y(x) y'(x)+2 y(x)+x=0$$

ODE
$3 x y'(x)^2-6 y(x) y'(x)+2 y(x)+x=0$ ODE Classiﬁcation

[[_homogeneous, class A], _rational, _dAlembert]

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

Mathematica
cpu = 0.237885 (sec), leaf count = 53

$\left \{\left \{y(x)\to \frac {1}{3} x \left (1+2 \cosh \left (-\log (x)+\sqrt {3} c_1\right )\right )\right \},\left \{y(x)\to \frac {1}{3} x \left (1+2 \cosh \left (\log (x)+\sqrt {3} c_1\right )\right )\right \}\right \}$

Maple
cpu = 0.086 (sec), leaf count = 40

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

DSolve[x + 2*y[x] - 6*y[x]*y'[x] + 3*x*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> (x*(1 + 2*Cosh[Sqrt[3]*C[1] - Log[x]]))/3}, {y[x] -> (x*(1 + 2*Cosh[Sq
rt[3]*C[1] + Log[x]]))/3}}

Maple raw input

dsolve(3*x*diff(y(x),x)^2-6*y(x)*diff(y(x),x)+x+2*y(x) = 0, y(x))

Maple raw output

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