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 = 600.065 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 4.72 (sec), leaf count = 389
\[\left [y \left (x \right ) = -\frac {\sqrt {-6-81 x^{2}-6 \sqrt {-216 x^{3}+108 x^{2}-18 x +1}+54 x}}{9}, y \left (x \right ) = \frac {\sqrt {-6-81 x^{2}-6 \sqrt {-216 x^{3}+108 x^{2}-18 x +1}+54 x}}{9}, y \left (x \right ) = -\frac {\sqrt {-6-81 x^{2}+6 \sqrt {-216 x^{3}+108 x^{2}-18 x +1}+54 x}}{9}, y \left (x \right ) = \frac {\sqrt {-6-81 x^{2}+6 \sqrt {-216 x^{3}+108 x^{2}-18 x +1}+54 x}}{9}, y \left (x \right ) = \sqrt {-\left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}+2 x \textit {\_C1} +\textit {\_C1}^{3}-x^{2}}, y \left (x \right ) = -\sqrt {-\left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}+2 x \textit {\_C1} +\textit {\_C1}^{3}-x^{2}}, y \left (x \right ) = -\frac {\sqrt {-2 i \sqrt {3}\, \left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}-4 i \sqrt {3}\, \textit {\_C1} x +2 \left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}-4 x \textit {\_C1} +4 \textit {\_C1}^{3}-4 x^{2}}}{2}, y \left (x \right ) = \frac {\sqrt {-2 i \sqrt {3}\, \left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}-4 i \sqrt {3}\, \textit {\_C1} x +2 \left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}-4 x \textit {\_C1} +4 \textit {\_C1}^{3}-4 x^{2}}}{2}, y \left (x \right ) = -\frac {\sqrt {2 i \sqrt {3}\, \left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}+4 i \sqrt {3}\, \textit {\_C1} x +2 \left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}-4 x \textit {\_C1} +4 \textit {\_C1}^{3}-4 x^{2}}}{2}, y \left (x \right ) = \frac {\sqrt {2 i \sqrt {3}\, \left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}+4 i \sqrt {3}\, \textit {\_C1} x +2 \left (\textit {\_C1}^{3}\right )^{\frac {2}{3}}-4 x \textit {\_C1} +4 \textit {\_C1}^{3}-4 x^{2}}}{2}\right ]\] 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))
Maple raw output
[y(x) = -1/9*(-6-81*x^2-6*(-216*x^3+108*x^2-18*x+1)^(1/2)+54*x)^(1/2), y(x) = 1/9*(-6-81*x^2-6*(-216*x^3+108*x^2-18*x+1)^(1/2)+54*x)^(1/2), y(x) = -1/9*(-6-81*x^2+6*(-216*x^3+108*x^2-18*x+1)^(1/2)+54*x)^(1/2), y(x) = 1/9*(-6-81*x^2+6*(-216*x^3+108*x^2-18*x+1)^(1/2)+54*x)^(1/2), y(x) = (-(_C1^3)^(2/3)+2*x*_C1+_C1^3-x^2)^(1/2), y(x) = -(-(_C1^3)^(2/3)+2*x*_C1+_C1^3-x^2)^(1/2), y(x) = -1/2*(-2*I*3^(1/2)*(_C1^3)^(2/3)-4*I*3^(1/2)*_C1*x+2*(_C1^3)^(2/3)-4*x*_C1+4*_C1^3-4*x^2)^(1/2), y(x) = 1/2*(-2*I*3^(1/2)*(_C1^3)^(2/3)-4*I*3^(1/2)*_C1*x+2*(_C1^3)^(2/3)-4*x*_C1+4*_C1^3-4*x^2)^(1/2), y(x) = -1/2*(2*I*3^(1/2)*(_C1^3)^(2/3)+4*I*3^(1/2)*_C1*x+2*(_C1^3)^(2/3)-4*x*_C1+4*_C1^3-4*x^2)^(1/2), y(x) = 1/2*(2*I*3^(1/2)*(_C1^3)^(2/3)+4*I*3^(1/2)*_C1*x+2*(_C1^3)^(2/3)-4*x*_C1+4*_C1^3-4*x^2)^(1/2)]