ODE
\[ y(x) y'(x)^3-3 x y'(x)+3 y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 47.1072 (sec), leaf count = 2640
\[\left \{\text {Solve}\left [c_1=\int _1^x\frac {4 y(x)^2 K[1]^4+2^{2/3} y(x)^3 \sqrt [3]{\sqrt {9 y(x)^6-4 K[1]^3 y(x)^3}-3 y(x)^3} K[1]^2+2^{2/3} \sqrt {9 y(x)^6-4 K[1]^3 y(x)^3} \sqrt [3]{\sqrt {9 y(x)^6-4 K[1]^3 y(x)^3}-3 y(x)^3} K[1]^2+3 \sqrt [3]{2} y(x)^4 \left (\sqrt {9 y(x)^6-4 K[1]^3 y(x)^3}-3 y(x)^3\right )^{2/3}+\sqrt [3]{2} y(x) \left (\sqrt {9 y(x)^6-4 K[1]^3 y(x)^3}-2 K[1]^3\right ) \left (\sqrt {9 y(x)^6-4 K[1]^3 y(x)^3}-3 y(x)^3\right )^{2/3}}{4 K[1]^2 y(x)^5}dK[1]+\int _1^{y(x)}-\frac {4 x \int _1^x\frac {-12 \sqrt [3]{2} K[2]^2 \sqrt [3]{\sqrt {9 K[2]^6-4 K[1]^3 K[2]^3}-3 K[2]^3} K[1]^4+6\ 2^{2/3} K[2] \left (\sqrt {9 K[2]^6-4 K[1]^3 K[2]^3}-2 K[2]^3\right ) K[1]^3-6 \sqrt {9 K[2]^6-4 K[1]^3 K[2]^3} \left (\sqrt {9 K[2]^6-4 K[1]^3 K[2]^3}-3 K[2]^3\right )^{2/3} K[1]^2-3 K[2]^2 \left (\sqrt {9 K[2]^6-4 K[1]^3 K[2]^3}-5 K[2]^3\right ) \sqrt [3]{2 \sqrt {9 K[2]^6-4 K[1]^3 K[2]^3}-6 K[2]^3} K[1]+3\ 2^{2/3} K[2]^4 \left (3 K[2]^3-\sqrt {9 K[2]^6-4 K[1]^3 K[2]^3}\right )}{2 K[2]^4 \sqrt {9 K[2]^6-4 K[1]^3 K[2]^3} \left (\sqrt {9 K[2]^6-4 K[1]^3 K[2]^3}-3 K[2]^3\right )^{2/3}}dK[1] K[2]^6-4 x K[2]^5+4 x^4 K[2]^2+\sqrt [3]{2} \left (\sqrt {9 K[2]^6-4 x^3 K[2]^3}-3 K[2]^3\right )^{2/3} \left (3 K[2]^3+\sqrt {9 K[2]^6-4 x^3 K[2]^3}\right ) K[2]-2 \sqrt [3]{2} x^3 \left (\sqrt {9 K[2]^6-4 x^3 K[2]^3}-3 K[2]^3\right )^{2/3} K[2]+2^{2/3} x^2 \sqrt [3]{\sqrt {9 K[2]^6-4 x^3 K[2]^3}-3 K[2]^3} \left (K[2]^3+\sqrt {9 K[2]^6-4 x^3 K[2]^3}\right )}{4 x K[2]^6}dK[2],y(x)\right ],\text {Solve}\left [c_1=\int _1^x\frac {8 y(x)^2 K[3]^4+2^{2/3} \left (-1-i \sqrt {3}\right ) y(x)^3 \sqrt [3]{\sqrt {9 y(x)^6-4 K[3]^3 y(x)^3}-3 y(x)^3} K[3]^2+2^{2/3} \left (-1-i \sqrt {3}\right ) \sqrt {9 y(x)^6-4 K[3]^3 y(x)^3} \sqrt [3]{\sqrt {9 y(x)^6-4 K[3]^3 y(x)^3}-3 y(x)^3} K[3]^2+3 i \sqrt [3]{2} \left (i+\sqrt {3}\right ) y(x)^4 \left (\sqrt {9 y(x)^6-4 K[3]^3 y(x)^3}-3 y(x)^3\right )^{2/3}+i \sqrt [3]{2} \left (i+\sqrt {3}\right ) y(x) \left (\sqrt {9 y(x)^6-4 K[3]^3 y(x)^3}-2 K[3]^3\right ) \left (\sqrt {9 y(x)^6-4 K[3]^3 y(x)^3}-3 y(x)^3\right )^{2/3}}{8 K[3]^2 y(x)^5}dK[3]+\int _1^{y(x)}\frac {-8 x \int _1^x\frac {12 \left (1-i \sqrt {3}\right ) K[4]^2 \sqrt [3]{2 \sqrt {9 K[4]^6-4 K[3]^3 K[4]^3}-6 K[4]^3} K[3]^4-6 i 2^{2/3} \left (-i+\sqrt {3}\right ) K[4] \left (\sqrt {9 K[4]^6-4 K[3]^3 K[4]^3}-2 K[4]^3\right ) K[3]^3-12 \sqrt {9 K[4]^6-4 K[3]^3 K[4]^3} \left (\sqrt {9 K[4]^6-4 K[3]^3 K[4]^3}-3 K[4]^3\right )^{2/3} K[3]^2+3 \left (1-i \sqrt {3}\right ) K[4]^2 \left (\sqrt {9 K[4]^6-4 K[3]^3 K[4]^3}-5 K[4]^3\right ) \sqrt [3]{2 \sqrt {9 K[4]^6-4 K[3]^3 K[4]^3}-6 K[4]^3} K[3]+3\ 2^{2/3} \left (1+i \sqrt {3}\right ) K[4]^4 \left (\sqrt {9 K[4]^6-4 K[3]^3 K[4]^3}-3 K[4]^3\right )}{4 K[4]^4 \sqrt {9 K[4]^6-4 K[3]^3 K[4]^3} \left (\sqrt {9 K[4]^6-4 K[3]^3 K[4]^3}-3 K[4]^3\right )^{2/3}}dK[3] K[4]^6+8 x K[4]^5-8 x^4 K[4]^2+\sqrt [3]{2} \left (1-i \sqrt {3}\right ) \left (\sqrt {9 K[4]^6-4 x^3 K[4]^3}-3 K[4]^3\right )^{2/3} \left (3 K[4]^3+\sqrt {9 K[4]^6-4 x^3 K[4]^3}\right ) K[4]+2 i \sqrt [3]{2} \left (i+\sqrt {3}\right ) x^3 \left (\sqrt {9 K[4]^6-4 x^3 K[4]^3}-3 K[4]^3\right )^{2/3} K[4]+2^{2/3} \left (1+i \sqrt {3}\right ) x^2 \sqrt [3]{\sqrt {9 K[4]^6-4 x^3 K[4]^3}-3 K[4]^3} \left (K[4]^3+\sqrt {9 K[4]^6-4 x^3 K[4]^3}\right )}{8 x K[4]^6}dK[4],y(x)\right ],\text {Solve}\left [c_1=\int _1^x\frac {8 y(x)^2 K[5]^4+i 2^{2/3} \left (i+\sqrt {3}\right ) y(x)^3 \sqrt [3]{\sqrt {9 y(x)^6-4 K[5]^3 y(x)^3}-3 y(x)^3} K[5]^2+i 2^{2/3} \left (i+\sqrt {3}\right ) \sqrt {9 y(x)^6-4 K[5]^3 y(x)^3} \sqrt [3]{\sqrt {9 y(x)^6-4 K[5]^3 y(x)^3}-3 y(x)^3} K[5]^2-3 i \sqrt [3]{2} \left (-i+\sqrt {3}\right ) y(x)^4 \left (\sqrt {9 y(x)^6-4 K[5]^3 y(x)^3}-3 y(x)^3\right )^{2/3}-i \sqrt [3]{2} \left (-i+\sqrt {3}\right ) y(x) \left (\sqrt {9 y(x)^6-4 K[5]^3 y(x)^3}-2 K[5]^3\right ) \left (\sqrt {9 y(x)^6-4 K[5]^3 y(x)^3}-3 y(x)^3\right )^{2/3}}{8 K[5]^2 y(x)^5}dK[5]+\int _1^{y(x)}\frac {-8 x \int _1^x\frac {12 \left (1+i \sqrt {3}\right ) K[6]^2 \sqrt [3]{2 \sqrt {9 K[6]^6-4 K[5]^3 K[6]^3}-6 K[6]^3} K[5]^4+6 i 2^{2/3} \left (i+\sqrt {3}\right ) K[6] \left (\sqrt {9 K[6]^6-4 K[5]^3 K[6]^3}-2 K[6]^3\right ) K[5]^3-12 \sqrt {9 K[6]^6-4 K[5]^3 K[6]^3} \left (\sqrt {9 K[6]^6-4 K[5]^3 K[6]^3}-3 K[6]^3\right )^{2/3} K[5]^2+3 \left (1+i \sqrt {3}\right ) K[6]^2 \left (\sqrt {9 K[6]^6-4 K[5]^3 K[6]^3}-5 K[6]^3\right ) \sqrt [3]{2 \sqrt {9 K[6]^6-4 K[5]^3 K[6]^3}-6 K[6]^3} K[5]+3\ 2^{2/3} \left (1-i \sqrt {3}\right ) K[6]^4 \left (\sqrt {9 K[6]^6-4 K[5]^3 K[6]^3}-3 K[6]^3\right )}{4 K[6]^4 \sqrt {9 K[6]^6-4 K[5]^3 K[6]^3} \left (\sqrt {9 K[6]^6-4 K[5]^3 K[6]^3}-3 K[6]^3\right )^{2/3}}dK[5] K[6]^6+8 x K[6]^5-8 x^4 K[6]^2+\sqrt [3]{2} \left (1+i \sqrt {3}\right ) \left (\sqrt {9 K[6]^6-4 x^3 K[6]^3}-3 K[6]^3\right )^{2/3} \left (3 K[6]^3+\sqrt {9 K[6]^6-4 x^3 K[6]^3}\right ) K[6]-2 i \sqrt [3]{2} \left (-i+\sqrt {3}\right ) x^3 \left (\sqrt {9 K[6]^6-4 x^3 K[6]^3}-3 K[6]^3\right )^{2/3} K[6]+2^{2/3} \left (1-i \sqrt {3}\right ) x^2 \sqrt [3]{\sqrt {9 K[6]^6-4 x^3 K[6]^3}-3 K[6]^3} \left (K[6]^3+\sqrt {9 K[6]^6-4 x^3 K[6]^3}\right )}{8 x K[6]^6}dK[6],y(x)\right ]\right \}\]
Maple ✓
cpu = 0.235 (sec), leaf count = 394
\[\left [y \left (x \right ) = \frac {3 \left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}} x}{\left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right ) \left (-\frac {3}{3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1}+3\right )}, y \left (x \right ) = \frac {3 \left (-\frac {\left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )}-\frac {i \sqrt {3}\, \left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )}\right ) x}{\left (-\frac {\left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )}-\frac {i \sqrt {3}\, \left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )}\right )^{3}+3}, y \left (x \right ) = \frac {3 \left (-\frac {\left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )}+\frac {i \sqrt {3}\, \left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}}}{6 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+2}\right ) x}{\left (-\frac {\left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )}+\frac {i \sqrt {3}\, \left (-3 \left (3 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+1\right )^{2}\right )^{\frac {1}{3}}}{6 \LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {1}{3}}}{3 \textit {\_C1}}\right )+2}\right )^{3}+3}\right ]\] Mathematica raw input
DSolve[3*y[x] - 3*x*y'[x] + y[x]*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{Solve[C[1] == Inactive[Integrate][(4*K[1]^4*y[x]^2 + 2^(2/3)*K[1]^2*y[x]^3*(-3*y[x]^3 + Sqrt[-4*K[1]^3*y[x]^3 + 9*y[x]^6])^(1/3) + 2^(2/3)*K[1]^2*Sqrt[-4*K[1]^3*y[x]^3 + 9*y[x]^6]*(-3*y[x]^3 + Sqrt[-4*K[1]^3*y[x]^3 + 9*y[x]^6])^(1/3) + 3*2^(1/3)*y[x]^4*(-3*y[x]^3 + Sqrt[-4*K[1]^3*y[x]^3 + 9*y[x]^6])^(2/3) + 2^(1/3)*y[x]*(-2*K[1]^3 + Sqrt[-4*K[1]^3*y[x]^3 + 9*y[x]^6])*(-3*y[x]^3 + Sqrt[-4*K[1]^3*y[x]^3 + 9*y[x]^6])^(2/3))/(4*K[1]^2*y[x]^5), {K[1], 1, x}] + Inactive[Integrate][-1/4*(4*x^4*K[2]^2 - 4*x*K[2]^5 - 2*2^(1/3)*x^3*K[2]*(-3*K[2]^3 + Sqrt[-4*x^3*K[2]^3 + 9*K[2]^6])^(2/3) + 2^(2/3)*x^2*(-3*K[2]^3 + Sqrt[-4*x^3*K[2]^3 + 9*K[2]^6])^(1/3)*(K[2]^3 + Sqrt[-4*x^3*K[2]^3 + 9*K[2]^6]) + 2^(1/3)*K[2]*(-3*K[2]^3 + Sqrt[-4*x^3*K[2]^3 + 9*K[2]^6])^(2/3)*(3*K[2]^3 + Sqrt[-4*x^3*K[2]^3 + 9*K[2]^6]) + 4*x*K[2]^6*Inactive[Integrate][(3*2^(2/3)*K[2]^4*(3*K[2]^3 - Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6]) - 12*2^(1/3)*K[1]^4*K[2]^2*(-3*K[2]^3 + Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6])^(1/3) - 6*K[1]^2*Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6]*(-3*K[2]^3 + Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6])^(2/3) + 6*2^(2/3)*K[1]^3*K[2]*(-2*K[2]^3 + Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6]) - 3*K[1]*K[2]^2*(-5*K[2]^3 + Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6])*(-6*K[2]^3 + 2*Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6])^(1/3))/(2*K[2]^4*Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6]*(-3*K[2]^3 + Sqrt[-4*K[1]^3*K[2]^3 + 9*K[2]^6])^(2/3)), {K[1], 1, x}])/(x*K[2]^6), {K[2], 1, y[x]}], y[x]], Solve[C[1] == Inactive[Integrate][(8*K[3]^4*y[x]^2 + 2^(2/3)*(-1 - I*Sqrt[3])*K[3]^2*y[x]^3*(-3*y[x]^3 + Sqrt[-4*K[3]^3*y[x]^3 + 9*y[x]^6])^(1/3) + 2^(2/3)*(-1 - I*Sqrt[3])*K[3]^2*Sqrt[-4*K[3]^3*y[x]^3 + 9*y[x]^6]*(-3*y[x]^3 + Sqrt[-4*K[3]^3*y[x]^3 + 9*y[x]^6])^(1/3) + (3*I)*2^(1/3)*(I + Sqrt[3])*y[x]^4*(-3*y[x]^3 + Sqrt[-4*K[3]^3*y[x]^3 + 9*y[x]^6])^(2/3) + I*2^(1/3)*(I + Sqrt[3])*y[x]*(-2*K[3]^3 + Sqrt[-4*K[3]^3*y[x]^3 + 9*y[x]^6])*(-3*y[x]^3 + Sqrt[-4*K[3]^3*y[x]^3 + 9*y[x]^6])^(2/3))/(8*K[3]^2*y[x]^5), {K[3], 1, x}] + Inactive[Integrate][(-8*x^4*K[4]^2 + 8*x*K[4]^5 + (2*I)*2^(1/3)*(I + Sqrt[3])*x^3*K[4]*(-3*K[4]^3 + Sqrt[-4*x^3*K[4]^3 + 9*K[4]^6])^(2/3) + 2^(2/3)*(1 + I*Sqrt[3])*x^2*(-3*K[4]^3 + Sqrt[-4*x^3*K[4]^3 + 9*K[4]^6])^(1/3)*(K[4]^3 + Sqrt[-4*x^3*K[4]^3 + 9*K[4]^6]) + 2^(1/3)*(1 - I*Sqrt[3])*K[4]*(-3*K[4]^3 + Sqrt[-4*x^3*K[4]^3 + 9*K[4]^6])^(2/3)*(3*K[4]^3 + Sqrt[-4*x^3*K[4]^3 + 9*K[4]^6]) - 8*x*K[4]^6*Inactive[Integrate][(-12*K[3]^2*Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6]*(-3*K[4]^3 + Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6])^(2/3) + 3*2^(2/3)*(1 + I*Sqrt[3])*K[4]^4*(-3*K[4]^3 + Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6]) - (6*I)*2^(2/3)*(-I + Sqrt[3])*K[3]^3*K[4]*(-2*K[4]^3 + Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6]) + 12*(1 - I*Sqrt[3])*K[3]^4*K[4]^2*(-6*K[4]^3 + 2*Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6])^(1/3) + 3*(1 - I*Sqrt[3])*K[3]*K[4]^2*(-5*K[4]^3 + Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6])*(-6*K[4]^3 + 2*Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6])^(1/3))/(4*K[4]^4*Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6]*(-3*K[4]^3 + Sqrt[-4*K[3]^3*K[4]^3 + 9*K[4]^6])^(2/3)), {K[3], 1, x}])/(8*x*K[4]^6), {K[4], 1, y[x]}], y[x]], Solve[C[1] == Inactive[Integrate][(8*K[5]^4*y[x]^2 + I*2^(2/3)*(I + Sqrt[3])*K[5]^2*y[x]^3*(-3*y[x]^3 + Sqrt[-4*K[5]^3*y[x]^3 + 9*y[x]^6])^(1/3) + I*2^(2/3)*(I + Sqrt[3])*K[5]^2*Sqrt[-4*K[5]^3*y[x]^3 + 9*y[x]^6]*(-3*y[x]^3 + Sqrt[-4*K[5]^3*y[x]^3 + 9*y[x]^6])^(1/3) - (3*I)*2^(1/3)*(-I + Sqrt[3])*y[x]^4*(-3*y[x]^3 + Sqrt[-4*K[5]^3*y[x]^3 + 9*y[x]^6])^(2/3) - I*2^(1/3)*(-I + Sqrt[3])*y[x]*(-2*K[5]^3 + Sqrt[-4*K[5]^3*y[x]^3 + 9*y[x]^6])*(-3*y[x]^3 + Sqrt[-4*K[5]^3*y[x]^3 + 9*y[x]^6])^(2/3))/(8*K[5]^2*y[x]^5), {K[5], 1, x}] + Inactive[Integrate][(-8*x^4*K[6]^2 + 8*x*K[6]^5 - (2*I)*2^(1/3)*(-I + Sqrt[3])*x^3*K[6]*(-3*K[6]^3 + Sqrt[-4*x^3*K[6]^3 + 9*K[6]^6])^(2/3) + 2^(2/3)*(1 - I*Sqrt[3])*x^2*(-3*K[6]^3 + Sqrt[-4*x^3*K[6]^3 + 9*K[6]^6])^(1/3)*(K[6]^3 + Sqrt[-4*x^3*K[6]^3 + 9*K[6]^6]) + 2^(1/3)*(1 + I*Sqrt[3])*K[6]*(-3*K[6]^3 + Sqrt[-4*x^3*K[6]^3 + 9*K[6]^6])^(2/3)*(3*K[6]^3 + Sqrt[-4*x^3*K[6]^3 + 9*K[6]^6]) - 8*x*K[6]^6*Inactive[Integrate][(-12*K[5]^2*Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6]*(-3*K[6]^3 + Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6])^(2/3) + 3*2^(2/3)*(1 - I*Sqrt[3])*K[6]^4*(-3*K[6]^3 + Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6]) + (6*I)*2^(2/3)*(I + Sqrt[3])*K[5]^3*K[6]*(-2*K[6]^3 + Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6]) + 12*(1 + I*Sqrt[3])*K[5]^4*K[6]^2*(-6*K[6]^3 + 2*Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6])^(1/3) + 3*(1 + I*Sqrt[3])*K[5]*K[6]^2*(-5*K[6]^3 + Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6])*(-6*K[6]^3 + 2*Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6])^(1/3))/(4*K[6]^4*Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6]*(-3*K[6]^3 + Sqrt[-4*K[5]^3*K[6]^3 + 9*K[6]^6])^(2/3)), {K[5], 1, x}])/(8*x*K[6]^6), {K[6], 1, y[x]}], y[x]]}
Maple raw input
dsolve(y(x)*diff(y(x),x)^3-3*x*diff(y(x),x)+3*y(x) = 0, y(x))
Maple raw output
[y(x) = 3/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3)*x/(-3/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)+3), y(x) = 3*(-1/2/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3)-1/2*I*3^(1/2)/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3))*x/((-1/2/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3)-1/2*I*3^(1/2)/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3))^3+3), y(x) = 3*(-1/2/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3)+1/2*I*3^(1/2)/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3))*x/((-1/2/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3)+1/2*I*3^(1/2)/(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)*(-3*(3*LambertW(-1/3*x/_C1*exp(-1/3))+1)^2)^(1/3))^3+3)]