ODE
\[ 4 x y'(x)^3-6 y(x) y'(x)^2+3 y(x)-x=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✗
cpu = 600.011 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.087 (sec), leaf count = 63
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}+xy \left ( x \right ) -{\frac {{x}^{2}}{2}}=0,y \left ( x \right ) =x,[x \left ( {\it \_T} \right ) =2\,{\it \_C1}\,{{\it \_T}}^{2}-{\it \_C1},y \left ( {\it \_T} \right ) ={\frac { \left ( 4\,{{\it \_T}}^{3}-1 \right ) \left ( 2\,{{\it \_T}}^{2}-1 \right ) {\it \_C1}}{6\,{{\it \_T}}^{2}-3}}] \right \} \] Mathematica raw input
DSolve[-x + 3*y[x] - 6*y[x]*y'[x]^2 + 4*x*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(4*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2-x+3*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x, y(x)^2+x*y(x)-1/2*x^2 = 0, [x(_T) = 2*_C1*_T^2-_C1, y(_T) = (4*_T^3-1)*(2*_T^2-1)*_C1/(6*_T^2-3)]