ODE
\[ y'(x)^3-y(x) y'(x)-x=0 \] ODE Classification
[_dAlembert]
Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)
Mathematica ✓
cpu = 120.477 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 1.263 (sec), leaf count = 861
\[\left [\frac {\textit {\_C1} \left (i \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}} \sqrt {3}-12 i \sqrt {3}\, y \left (x \right )+\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}+12 y \left (x \right )\right )}{\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}} \sqrt {\frac {i \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {4}{3}} \sqrt {3}-144 i \sqrt {3}\, y \left (x \right )^{2}-\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {4}{3}}+48 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}} y \left (x \right )+72 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}-144 y \left (x \right )^{2}}{\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}}}}+x +\frac {i \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}} \sqrt {3}-12 i \sqrt {3}\, y \left (x \right )+\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}+12 y \left (x \right )}{6 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}}} = 0, \frac {\left (3 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}+36 y \left (x \right )\right ) \textit {\_C1}}{\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}} \sqrt {\frac {\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {4}{3}}+24 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}} y \left (x \right )+36 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}+144 y \left (x \right )^{2}}{\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}}}}+x -\frac {\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}+12 y \left (x \right )}{3 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}}} = 0, \frac {\left (6 i \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}} \sqrt {3}-72 i \sqrt {3}\, y \left (x \right )-6 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}-72 y \left (x \right )\right ) \textit {\_C1}}{\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}} \sqrt {\frac {-2 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {4}{3}}+96 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}} y \left (x \right )-288 y \left (x \right )^{2}-2 i \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {4}{3}} \sqrt {3}+288 i \sqrt {3}\, y \left (x \right )^{2}+144 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}}{\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}}}}+x -\frac {i \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}} \sqrt {3}-12 i \sqrt {3}\, y \left (x \right )-\left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}-12 y \left (x \right )}{6 \left (108 x +12 \sqrt {-12 y \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}}} = 0\right ]\] Mathematica raw input
DSolve[-x - y[x]*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3-y(x)*diff(y(x),x)-x = 0, y(x))
Maple raw output
[_C1*(I*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)*3^(1/2)-12*I*3^(1/2)*y(x)+(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)+12*y(x))/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(1/3)/((I*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(4/3)*3^(1/2)-144*I*3^(1/2)*y(x)^2-(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(4/3)+48*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)*y(x)+72*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)-144*y(x)^2)/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3))^(1/2)+x+1/6*(I*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)*3^(1/2)-12*I*3^(1/2)*y(x)+(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)+12*y(x))/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(1/3) = 0, (3*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)+36*y(x))/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(1/3)/(((108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(4/3)+24*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)*y(x)+36*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)+144*y(x)^2)/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3))^(1/2)*_C1+x-1/3*((108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)+12*y(x))/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(1/3) = 0, (6*I*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)*3^(1/2)-72*I*3^(1/2)*y(x)-6*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)-72*y(x))/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(1/3)/((-2*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(4/3)+96*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)*y(x)-288*y(x)^2-2*I*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(4/3)*3^(1/2)+288*I*3^(1/2)*y(x)^2+144*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3))/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3))^(1/2)*_C1+x-1/6*(I*(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)*3^(1/2)-12*I*3^(1/2)*y(x)-(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(2/3)-12*y(x))/(108*x+12*(-12*y(x)^3+81*x^2)^(1/2))^(1/3) = 0]