ODE
\[ y'(x)^4-3 (1-x) y'(x)^2+3 (1-2 y(x)) y'(x)+3 x=0 \] ODE Classification
[_dAlembert]
Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)
Mathematica ✗
cpu = 600.001 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.127 (sec), leaf count = 49
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) -{x}^{2}+{\frac {2\,x}{3}}+{\frac {5}{36}}=0,[x \left ( {\it \_T} \right ) ={\it \_T}\, \left ( {\it \_T}+{\it \_C1} \right ) ,y \left ( {\it \_T} \right ) ={\frac {{\it \_C1}\,{{\it \_T}}^{2}}{2}}+{\frac {2\,{{\it \_T}}^{3}}{3}}+{\frac {{\it \_C1}}{2}}+{\frac {1}{2}}] \right \} \] Mathematica raw input
DSolve[3*x + 3*(1 - 2*y[x])*y'[x] - 3*(1 - x)*y'[x]^2 + y'[x]^4 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^4-3*(1-x)*diff(y(x),x)^2+3*(1-2*y(x))*diff(y(x),x)+3*x = 0, y(x),'implicit')
Maple raw output
y(x)^2-y(x)-x^2+2/3*x+5/36 = 0, [x(_T) = _T*(_T+_C1), y(_T) = 1/2*_C1*_T^2+2/3*_T^3+1/2*_C1+1/2]