ODE
\[ 8 x^3 y'(x)^3+12 x^2 y(x) y'(x)^2-\left (1-6 x y(x)^2\right ) y'(x)+y(x)^3=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)
Mathematica ✗
cpu = 599.999 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.746 (sec), leaf count = 140
\[ \left \{ [x \left ( {\it \_T} \right ) ={1 \left ( {\frac {\ln \left ( {\it \_T} \right ) }{9}}+{\it \_C1} \right ) {{\it \_T}}^{-{\frac {2}{3}}}},y \left ( {\it \_T} \right ) =-{\frac {2\,\ln \left ( {\it \_T} \right ) +18\,{\it \_C1}-9}{9}\sqrt [3]{{\it \_T}}}],[x \left ( {\it \_T} \right ) =-{\frac {i\ln \left ( {\it \_T} \right ) \sqrt {3}-18\,{\it \_C1}+\ln \left ( {\it \_T} \right ) }{18}{{\it \_T}}^{-{\frac {2}{3}}}},y \left ( {\it \_T} \right ) ={\frac { \left ( 2\,i\ln \left ( {\it \_T} \right ) -9\,i \right ) \sqrt {3}-36\,{\it \_C1}+2\,\ln \left ( {\it \_T} \right ) -9}{18}\sqrt [3]{{\it \_T}}}],[x \left ( {\it \_T} \right ) ={\frac {i\ln \left ( {\it \_T} \right ) \sqrt {3}-\ln \left ( {\it \_T} \right ) +18\,{\it \_C1}}{18}{{\it \_T}}^{-{\frac {2}{3}}}},y \left ( {\it \_T} \right ) =-{\frac {2\,i\ln \left ( {\it \_T} \right ) \sqrt {3}-9\,i\sqrt {3}-2\,\ln \left ( {\it \_T} \right ) +36\,{\it \_C1}+9}{18}\sqrt [3]{{\it \_T}}}] \right \} \] Mathematica raw input
DSolve[y[x]^3 - (1 - 6*x*y[x]^2)*y'[x] + 12*x^2*y[x]*y'[x]^2 + 8*x^3*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(8*x^3*diff(y(x),x)^3+12*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x)^2)*diff(y(x),x)+y(x)^3 = 0, y(x),'implicit')
Maple raw output
[x(_T) = 1/_T^(2/3)*(1/9*ln(_T)+_C1), y(_T) = -1/9*_T^(1/3)*(2*ln(_T)+18*_C1-9)], [x(_T) = -1/18*(I*ln(_T)*3^(1/2)-18*_C1+ln(_T))/_T^(2/3), y(_T) = 1/18*((2*I*ln(_T)-9*I)*3^(1/2)-36*_C1+2*ln(_T)-9)*_T^(1/3)], [x(_T) = 1/18*(I*ln(_T)*3^(1/2)-ln(_T)+18*_C1)/_T^(2/3), y(_T) = -1/18*_T^(1/3)*(2*I*ln(_T)*3^(1/2)-9*I*3^(1/2)-2*ln(_T)+36*_C1+9)]