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 = 0.0732727 (sec), leaf count = 53

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

Maple
cpu = 0.033 (sec), leaf count = 53

\[ \left \{ -{\frac { \left (x+3\,y \relax (x ) \right ) \left (x-y \relax (x ) \right ) }{3}}=0,[x \left ({\it \_T} \right ) =3\,{\it \_C1}\,{\it \_T}-{\it \_C1},y \left ({\it \_T} \right ) ={\frac { \left (3\,{{\it \_T}}^{2}+1 \right ) \left (3\,{\it \_T}-1 \right ) {\it \_C1}}{6\,{\it \_T}-2}}] \right \} \] 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),'implicit')

Maple raw output

-1/3*(x+3*y(x))*(x-y(x)) = 0, [x(_T) = 3*_C1*_T-_C1, y(_T) = (3*_T^2+1)*(3*_T-1)
*_C1/(6*_T-2)]