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