ODE
\[ x^3+3 x^2 y(x) y'(x)+y(x)^3 y'(x)^3-(1-3 x) y(x)^2 y'(x)^2-y(x)^2=0 \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of variable
Mathematica ✗
cpu = 600. (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.647 (sec), leaf count = 176
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{4}+{\frac { \left ( 54\,{x}^{2}-36\,x+4 \right ) \left ( y \left ( x \right ) \right ) ^{2}}{27}}+{x}^{4}-{\frac {4\,{x}^{3}}{27}}=0,[x \left ( {\it \_T} \right ) ={1 \left ( \sqrt [3]{{{\it \_C1}}^{2}}\sqrt {{{\it \_T}}^{2}+1}-{\it \_C1}\,{\it \_T} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) ={{\it \_C1}{\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}],[x \left ( {\it \_T} \right ) ={\frac {1}{2} \left ( \sqrt [3]{{{\it \_C1}}^{2}} \left ( i\sqrt {3}-1 \right ) \sqrt {{{\it \_T}}^{2}+1}-2\,{\it \_C1}\,{\it \_T} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) ={{\it \_C1}{\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}],[x \left ( {\it \_T} \right ) =-{\frac {1}{2} \left ( \left ( i\sqrt {3}+1 \right ) \sqrt [3]{{{\it \_C1}}^{2}}\sqrt {{{\it \_T}}^{2}+1}+2\,{\it \_C1}\,{\it \_T} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) ={{\it \_C1}{\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}] \right \} \] Mathematica raw input
DSolve[x^3 - y[x]^2 + 3*x^2*y[x]*y'[x] - (1 - 3*x)*y[x]^2*y'[x]^2 + y[x]^3*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(y(x)^3*diff(y(x),x)^3-(1-3*x)*y(x)^2*diff(y(x),x)^2+3*x^2*y(x)*diff(y(x),x)+x^3-y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x)^4+1/27*(54*x^2-36*x+4)*y(x)^2+x^4-4/27*x^3 = 0, [x(_T) = ((_C1^2)^(1/3)*(_T^2+1)^(1/2)-_C1*_T)/(_T^2+1)^(1/2), y(_T) = _C1/(_T^2+1)^(1/2)], [x(_T) = -1/2*((I*3^(1/2)+1)*(_C1^2)^(1/3)*(_T^2+1)^(1/2)+2*_C1*_T)/(_T^2+1)^(1/2), y(_T) = _C1/(_T^2+1)^(1/2)], [x(_T) = 1/2*((_C1^2)^(1/3)*(I*3^(1/2)-1)*(_T^2+1)^(1/2)-2*_C1*_T)/(_T^2+1)^(1/2), y(_T) = _C1/(_T^2+1)^(1/2)]