ODE
\[ y'(x)^3-2 x y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 404.358 (sec), leaf count = 3278
\[\left \{\text {Solve}\left [c_1=\int _1^x\frac {4 \left (144 K[1]^2+4 \sqrt [3]{2} 3^{2/3} \left (\sqrt {81 y(x)^2-96 K[1]^3}-9 y(x)\right )^{2/3} K[1]-2^{2/3} 3^{5/6} \sqrt {27 y(x)^2-32 K[1]^3} \sqrt [3]{\sqrt {81 y(x)^2-96 K[1]^3}-9 y(x)}\right ) K[1]^2+y(x) \left (9 \sqrt [3]{2} \sqrt [6]{3} \sqrt {27 y(x)^2-32 K[1]^3} \left (\sqrt {81 y(x)^2-96 K[1]^3}-9 y(x)\right )^{2/3}-108\ 2^{2/3} \sqrt [3]{3} K[1]^2 \sqrt [3]{\sqrt {81 y(x)^2-96 K[1]^3}-9 y(x)}\right )+27 \sqrt [3]{2} 3^{2/3} y(x)^2 \left (\sqrt {81 y(x)^2-96 K[1]^3}-9 y(x)\right )^{2/3}}{768 K[1]^5-648 K[1]^2 y(x)^2}dK[1]+\int _1^{y(x)}\frac {128\ 2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 K[2]^2-96 x^3}-9 K[2]} x^5-192 \sqrt {27 K[2]^2-32 x^3} x^4+16 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {81 K[2]^2-96 x^3}-18 K[2]\right ) \left (\sqrt {81 K[2]^2-96 x^3}-9 K[2]\right )^{2/3} x^3-108\ 2^{2/3} \sqrt [3]{3} K[2] \left (\sqrt {3} K[2]+\sqrt {27 K[2]^2-32 x^3}\right ) \sqrt [3]{\sqrt {81 K[2]^2-96 x^3}-9 K[2]} x^2-36 K[2] \left (27 K[2]^2-32 x^3\right )^{3/2} \int _1^x\frac {2 \left (2048\ 2^{2/3} 3^{5/6} K[1]^6-64 \sqrt [3]{2} \sqrt [6]{3} \sqrt [3]{\sqrt {81 K[2]^2-96 K[1]^3}-9 K[2]} \left (27 K[2]+4 \sqrt {81 K[2]^2-96 K[1]^3}\right ) K[1]^4-144\ 2^{2/3} \sqrt [3]{3} K[2] \left (6 \sqrt {3} K[2]-7 \sqrt {27 K[2]^2-32 K[1]^3}\right ) K[1]^3+648 K[2] \sqrt {27 K[2]^2-32 K[1]^3} \left (\sqrt {81 K[2]^2-96 K[1]^3}-9 K[2]\right )^{2/3} K[1]^2-54 \sqrt [3]{2} \sqrt [6]{3} K[2]^2 \sqrt [3]{\sqrt {81 K[2]^2-96 K[1]^3}-9 K[2]} \left (5 \sqrt {81 K[2]^2-96 K[1]^3}-27 K[2]\right ) K[1]+243\ 2^{2/3} \sqrt [3]{3} K[2]^3 \left (\sqrt {27 K[2]^2-32 K[1]^3}-3 \sqrt {3} K[2]\right )\right )}{\left (27 K[2]^2-32 K[1]^3\right )^{5/2} \left (\sqrt {81 K[2]^2-96 K[1]^3}-9 K[2]\right )^{2/3}}dK[1] x+648 K[2]^2 \sqrt {27 K[2]^2-32 x^3} x+27 \sqrt [3]{2} \sqrt [6]{3} K[2]^2 \left (\sqrt {81 K[2]^2-96 x^3}-9 K[2]\right )^{2/3} \left (9 K[2]+\sqrt {81 K[2]^2-96 x^3}\right )}{36 x K[2] \left (27 K[2]^2-32 x^3\right )^{3/2}}dK[2],y(x)\right ],\text {Solve}\left [c_1=\int _1^x\frac {4 \left (288 K[3]^2-4 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) \left (\sqrt {81 y(x)^2-96 K[3]^3}-9 y(x)\right )^{2/3} K[3]+2^{2/3} \sqrt [3]{3} \left (-3 i+\sqrt {3}\right ) \sqrt {27 y(x)^2-32 K[3]^3} \sqrt [3]{\sqrt {81 y(x)^2-96 K[3]^3}-9 y(x)}\right ) K[3]^2+9 y(x) \left (12\ 2^{2/3} \sqrt [3]{3} \left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {81 y(x)^2-96 K[3]^3}-9 y(x)} K[3]^2+\sqrt [3]{2} \sqrt [6]{3} \left (-1-i \sqrt {3}\right ) \sqrt {27 y(x)^2-32 K[3]^3} \left (\sqrt {81 y(x)^2-96 K[3]^3}-9 y(x)\right )^{2/3}\right )-27 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) y(x)^2 \left (\sqrt {81 y(x)^2-96 K[3]^3}-9 y(x)\right )^{2/3}}{48 K[3]^2 \left (32 K[3]^3-27 y(x)^2\right )}dK[3]+\int _1^{y(x)}\frac {-128 2^{2/3} \sqrt [3]{3} \left (-3 i+\sqrt {3}\right ) \sqrt [3]{\sqrt {81 K[4]^2-96 x^3}-9 K[4]} x^5-384 \sqrt {27 K[4]^2-32 x^3} x^4-16 \sqrt [3]{2} \sqrt [6]{3} \left (\left (3 i+\sqrt {3}\right ) \sqrt {27 K[4]^2-32 x^3}-18 i \left (-i+\sqrt {3}\right ) K[4]\right ) \left (\sqrt {81 K[4]^2-96 x^3}-9 K[4]\right )^{2/3} x^3+108\ 2^{2/3} \sqrt [3]{3} K[4] \left (\left (-3 i+\sqrt {3}\right ) K[4]+\left (1-i \sqrt {3}\right ) \sqrt {27 K[4]^2-32 x^3}\right ) \sqrt [3]{\sqrt {81 K[4]^2-96 x^3}-9 K[4]} x^2-72 K[4] \left (27 K[4]^2-32 x^3\right )^{3/2} \int _1^x\frac {-2048 2^{2/3} \sqrt [3]{3} \left (-3 i+\sqrt {3}\right ) K[3]^6+64 \sqrt [3]{2} \sqrt [6]{3} \left (27 \left (1+i \sqrt {3}\right ) K[4]+4 \left (3 i+\sqrt {3}\right ) \sqrt {27 K[4]^2-32 K[3]^3}\right ) \sqrt [3]{\sqrt {81 K[4]^2-96 K[3]^3}-9 K[4]} K[3]^4+144\ 2^{2/3} \sqrt [3]{3} K[4] \left (6 \left (-3 i+\sqrt {3}\right ) K[4]+7 i \left (i+\sqrt {3}\right ) \sqrt {27 K[4]^2-32 K[3]^3}\right ) K[3]^3+1296 K[4] \sqrt {27 K[4]^2-32 K[3]^3} \left (\sqrt {81 K[4]^2-96 K[3]^3}-9 K[4]\right )^{2/3} K[3]^2+54 \sqrt [3]{2} \sqrt [6]{3} K[4]^2 \left (5 \left (3 i+\sqrt {3}\right ) \sqrt {27 K[4]^2-32 K[3]^3}-27 i \left (-i+\sqrt {3}\right ) K[4]\right ) \sqrt [3]{\sqrt {81 K[4]^2-96 K[3]^3}-9 K[4]} K[3]+243\ 2^{2/3} \sqrt [3]{3} K[4]^3 \left (3 \left (-3 i+\sqrt {3}\right ) K[4]+i \left (i+\sqrt {3}\right ) \sqrt {27 K[4]^2-32 K[3]^3}\right )}{\left (27 K[4]^2-32 K[3]^3\right )^{5/2} \left (\sqrt {81 K[4]^2-96 K[3]^3}-9 K[4]\right )^{2/3}}dK[3] x+1296 K[4]^2 \sqrt {27 K[4]^2-32 x^3} x-27 \sqrt [3]{2} \sqrt [6]{3} K[4]^2 \left (\left (9+9 i \sqrt {3}\right ) K[4]+\left (3 i+\sqrt {3}\right ) \sqrt {27 K[4]^2-32 x^3}\right ) \left (\sqrt {81 K[4]^2-96 x^3}-9 K[4]\right )^{2/3}}{72 x K[4] \left (27 K[4]^2-32 x^3\right )^{3/2}}dK[4],y(x)\right ],\text {Solve}\left [c_1=\int _1^x\frac {4 \left (288 K[5]^2-4 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) \left (\sqrt {81 y(x)^2-96 K[5]^3}-9 y(x)\right )^{2/3} K[5]+2^{2/3} \sqrt [3]{3} \left (3 i+\sqrt {3}\right ) \sqrt {27 y(x)^2-32 K[5]^3} \sqrt [3]{\sqrt {81 y(x)^2-96 K[5]^3}-9 y(x)}\right ) K[5]^2+9 y(x) \left (12\ 2^{2/3} \sqrt [3]{3} \left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {81 y(x)^2-96 K[5]^3}-9 y(x)} K[5]^2+i \sqrt [3]{2} \sqrt [6]{3} \left (i+\sqrt {3}\right ) \sqrt {27 y(x)^2-32 K[5]^3} \left (\sqrt {81 y(x)^2-96 K[5]^3}-9 y(x)\right )^{2/3}\right )-27 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) y(x)^2 \left (\sqrt {81 y(x)^2-96 K[5]^3}-9 y(x)\right )^{2/3}}{48 K[5]^2 \left (32 K[5]^3-27 y(x)^2\right )}dK[5]+\int _1^{y(x)}\frac {-128 2^{2/3} \sqrt [3]{3} \left (3 i+\sqrt {3}\right ) \sqrt [3]{\sqrt {81 K[6]^2-96 x^3}-9 K[6]} x^5-384 \sqrt {27 K[6]^2-32 x^3} x^4-16 \sqrt [3]{2} \sqrt [6]{3} \left (18 i \left (i+\sqrt {3}\right ) K[6]+\left (-3 i+\sqrt {3}\right ) \sqrt {27 K[6]^2-32 x^3}\right ) \left (\sqrt {81 K[6]^2-96 x^3}-9 K[6]\right )^{2/3} x^3+108\ 2^{2/3} \sqrt [3]{3} K[6] \left (\left (3 i+\sqrt {3}\right ) K[6]+\left (1+i \sqrt {3}\right ) \sqrt {27 K[6]^2-32 x^3}\right ) \sqrt [3]{\sqrt {81 K[6]^2-96 x^3}-9 K[6]} x^2-72 K[6] \left (27 K[6]^2-32 x^3\right )^{3/2} \int _1^x\frac {-2048 2^{2/3} \sqrt [3]{3} \left (3 i+\sqrt {3}\right ) K[5]^6+64 \sqrt [3]{2} \sqrt [6]{3} \left (27 \left (1-i \sqrt {3}\right ) K[6]+4 \left (-3 i+\sqrt {3}\right ) \sqrt {27 K[6]^2-32 K[5]^3}\right ) \sqrt [3]{\sqrt {81 K[6]^2-96 K[5]^3}-9 K[6]} K[5]^4+144\ 2^{2/3} \sqrt [3]{3} K[6] \left (6 \left (3 i+\sqrt {3}\right ) K[6]-7 i \left (-i+\sqrt {3}\right ) \sqrt {27 K[6]^2-32 K[5]^3}\right ) K[5]^3+1296 K[6] \sqrt {27 K[6]^2-32 K[5]^3} \left (\sqrt {81 K[6]^2-96 K[5]^3}-9 K[6]\right )^{2/3} K[5]^2+54 \sqrt [3]{2} \sqrt [6]{3} K[6]^2 \left (27 i \left (i+\sqrt {3}\right ) K[6]+5 \left (-3 i+\sqrt {3}\right ) \sqrt {27 K[6]^2-32 K[5]^3}\right ) \sqrt [3]{\sqrt {81 K[6]^2-96 K[5]^3}-9 K[6]} K[5]+243\ 2^{2/3} \sqrt [3]{3} K[6]^3 \left (3 \left (3 i+\sqrt {3}\right ) K[6]+\left (-1-i \sqrt {3}\right ) \sqrt {27 K[6]^2-32 K[5]^3}\right )}{\left (27 K[6]^2-32 K[5]^3\right )^{5/2} \left (\sqrt {81 K[6]^2-96 K[5]^3}-9 K[6]\right )^{2/3}}dK[5] x+1296 K[6]^2 \sqrt {27 K[6]^2-32 x^3} x-27 \sqrt [3]{2} \sqrt [6]{3} K[6]^2 \left (\left (9-9 i \sqrt {3}\right ) K[6]+\left (-3 i+\sqrt {3}\right ) \sqrt {27 K[6]^2-32 x^3}\right ) \left (\sqrt {81 K[6]^2-96 x^3}-9 K[6]\right )^{2/3}}{72 x K[6] \left (27 K[6]^2-32 x^3\right )^{3/2}}dK[6],y(x)\right ]\right \}\]
Maple ✓
cpu = 0.089 (sec), leaf count = 496
\[\left [-\frac {\textit {\_C1}}{\left (\frac {\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}+24 x}{\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {1}{3}}}\right )^{\frac {2}{3}}}+x -\frac {\left (\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}+24 x \right )^{2}}{96 \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}} = 0, -\frac {\textit {\_C1}}{\left (\frac {i \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}} \sqrt {3}-24 i \sqrt {3}\, x -\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}-24 x}{\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {1}{3}}}\right )^{\frac {2}{3}}}+x -\frac {\left (i \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}} \sqrt {3}-24 i \sqrt {3}\, x -\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}-24 x \right )^{2}}{384 \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}} = 0, -\frac {12^{\frac {2}{3}} \textit {\_C1}}{\left (\frac {-i \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}} \sqrt {3}+24 i \sqrt {3}\, x -\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}-24 x}{\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {1}{3}}}\right )^{\frac {2}{3}}}+x -\frac {\left (i \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}} \sqrt {3}-24 i \sqrt {3}\, x +\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}+24 x \right )^{2}}{384 \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}} = 0\right ]\] Mathematica raw input
DSolve[-y[x] - 2*x*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{Solve[C[1] == Inactive[Integrate][(27*2^(1/3)*3^(2/3)*y[x]^2*(-9*y[x] + Sqrt[-96*K[1]^3 + 81*y[x]^2])^(2/3) + 4*K[1]^2*(144*K[1]^2 - 2^(2/3)*3^(5/6)*Sqrt[-32*K[1]^3 + 27*y[x]^2]*(-9*y[x] + Sqrt[-96*K[1]^3 + 81*y[x]^2])^(1/3) + 4*2^(1/3)*3^(2/3)*K[1]*(-9*y[x] + Sqrt[-96*K[1]^3 + 81*y[x]^2])^(2/3)) + y[x]*(-108*2^(2/3)*3^(1/3)*K[1]^2*(-9*y[x] + Sqrt[-96*K[1]^3 + 81*y[x]^2])^(1/3) + 9*2^(1/3)*3^(1/6)*Sqrt[-32*K[1]^3 + 27*y[x]^2]*(-9*y[x] + Sqrt[-96*K[1]^3 + 81*y[x]^2])^(2/3)))/(768*K[1]^5 - 648*K[1]^2*y[x]^2), {K[1], 1, x}] + Inactive[Integrate][(-192*x^4*Sqrt[-32*x^3 + 27*K[2]^2] + 648*x*K[2]^2*Sqrt[-32*x^3 + 27*K[2]^2] + 128*2^(2/3)*3^(5/6)*x^5*(-9*K[2] + Sqrt[-96*x^3 + 81*K[2]^2])^(1/3) - 108*2^(2/3)*3^(1/3)*x^2*K[2]*(Sqrt[3]*K[2] + Sqrt[-32*x^3 + 27*K[2]^2])*(-9*K[2] + Sqrt[-96*x^3 + 81*K[2]^2])^(1/3) + 16*2^(1/3)*3^(1/6)*x^3*(-18*K[2] + Sqrt[-96*x^3 + 81*K[2]^2])*(-9*K[2] + Sqrt[-96*x^3 + 81*K[2]^2])^(2/3) + 27*2^(1/3)*3^(1/6)*K[2]^2*(-9*K[2] + Sqrt[-96*x^3 + 81*K[2]^2])^(2/3)*(9*K[2] + Sqrt[-96*x^3 + 81*K[2]^2]) - 36*x*K[2]*(-32*x^3 + 27*K[2]^2)^(3/2)*Inactive[Integrate][(2*(2048*2^(2/3)*3^(5/6)*K[1]^6 - 144*2^(2/3)*3^(1/3)*K[1]^3*K[2]*(6*Sqrt[3]*K[2] - 7*Sqrt[-32*K[1]^3 + 27*K[2]^2]) + 243*2^(2/3)*3^(1/3)*K[2]^3*(-3*Sqrt[3]*K[2] + Sqrt[-32*K[1]^3 + 27*K[2]^2]) + 648*K[1]^2*K[2]*Sqrt[-32*K[1]^3 + 27*K[2]^2]*(-9*K[2] + Sqrt[-96*K[1]^3 + 81*K[2]^2])^(2/3) - 64*2^(1/3)*3^(1/6)*K[1]^4*(-9*K[2] + Sqrt[-96*K[1]^3 + 81*K[2]^2])^(1/3)*(27*K[2] + 4*Sqrt[-96*K[1]^3 + 81*K[2]^2]) - 54*2^(1/3)*3^(1/6)*K[1]*K[2]^2*(-9*K[2] + Sqrt[-96*K[1]^3 + 81*K[2]^2])^(1/3)*(-27*K[2] + 5*Sqrt[-96*K[1]^3 + 81*K[2]^2])))/((-32*K[1]^3 + 27*K[2]^2)^(5/2)*(-9*K[2] + Sqrt[-96*K[1]^3 + 81*K[2]^2])^(2/3)), {K[1], 1, x}])/(36*x*K[2]*(-32*x^3 + 27*K[2]^2)^(3/2)), {K[2], 1, y[x]}], y[x]], Solve[C[1] == Inactive[Integrate][(-27*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*y[x]^2*(-9*y[x] + Sqrt[-96*K[3]^3 + 81*y[x]^2])^(2/3) + 4*K[3]^2*(288*K[3]^2 + 2^(2/3)*3^(1/3)*(-3*I + Sqrt[3])*Sqrt[-32*K[3]^3 + 27*y[x]^2]*(-9*y[x] + Sqrt[-96*K[3]^3 + 81*y[x]^2])^(1/3) - 4*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*K[3]*(-9*y[x] + Sqrt[-96*K[3]^3 + 81*y[x]^2])^(2/3)) + 9*y[x]*(12*2^(2/3)*3^(1/3)*(1 - I*Sqrt[3])*K[3]^2*(-9*y[x] + Sqrt[-96*K[3]^3 + 81*y[x]^2])^(1/3) + 2^(1/3)*3^(1/6)*(-1 - I*Sqrt[3])*Sqrt[-32*K[3]^3 + 27*y[x]^2]*(-9*y[x] + Sqrt[-96*K[3]^3 + 81*y[x]^2])^(2/3)))/(48*K[3]^2*(32*K[3]^3 - 27*y[x]^2)), {K[3], 1, x}] + Inactive[Integrate][(-384*x^4*Sqrt[-32*x^3 + 27*K[4]^2] + 1296*x*K[4]^2*Sqrt[-32*x^3 + 27*K[4]^2] - 128*2^(2/3)*3^(1/3)*(-3*I + Sqrt[3])*x^5*(-9*K[4] + Sqrt[-96*x^3 + 81*K[4]^2])^(1/3) + 108*2^(2/3)*3^(1/3)*x^2*K[4]*((-3*I + Sqrt[3])*K[4] + (1 - I*Sqrt[3])*Sqrt[-32*x^3 + 27*K[4]^2])*(-9*K[4] + Sqrt[-96*x^3 + 81*K[4]^2])^(1/3) - 27*2^(1/3)*3^(1/6)*K[4]^2*((9 + (9*I)*Sqrt[3])*K[4] + (3*I + Sqrt[3])*Sqrt[-32*x^3 + 27*K[4]^2])*(-9*K[4] + Sqrt[-96*x^3 + 81*K[4]^2])^(2/3) - 16*2^(1/3)*3^(1/6)*x^3*((-18*I)*(-I + Sqrt[3])*K[4] + (3*I + Sqrt[3])*Sqrt[-32*x^3 + 27*K[4]^2])*(-9*K[4] + Sqrt[-96*x^3 + 81*K[4]^2])^(2/3) - 72*x*K[4]*(-32*x^3 + 27*K[4]^2)^(3/2)*Inactive[Integrate][(-2048*2^(2/3)*3^(1/3)*(-3*I + Sqrt[3])*K[3]^6 + 243*2^(2/3)*3^(1/3)*K[4]^3*(3*(-3*I + Sqrt[3])*K[4] + I*(I + Sqrt[3])*Sqrt[-32*K[3]^3 + 27*K[4]^2]) + 144*2^(2/3)*3^(1/3)*K[3]^3*K[4]*(6*(-3*I + Sqrt[3])*K[4] + (7*I)*(I + Sqrt[3])*Sqrt[-32*K[3]^3 + 27*K[4]^2]) + 64*2^(1/3)*3^(1/6)*K[3]^4*(27*(1 + I*Sqrt[3])*K[4] + 4*(3*I + Sqrt[3])*Sqrt[-32*K[3]^3 + 27*K[4]^2])*(-9*K[4] + Sqrt[-96*K[3]^3 + 81*K[4]^2])^(1/3) + 54*2^(1/3)*3^(1/6)*K[3]*K[4]^2*((-27*I)*(-I + Sqrt[3])*K[4] + 5*(3*I + Sqrt[3])*Sqrt[-32*K[3]^3 + 27*K[4]^2])*(-9*K[4] + Sqrt[-96*K[3]^3 + 81*K[4]^2])^(1/3) + 1296*K[3]^2*K[4]*Sqrt[-32*K[3]^3 + 27*K[4]^2]*(-9*K[4] + Sqrt[-96*K[3]^3 + 81*K[4]^2])^(2/3))/((-32*K[3]^3 + 27*K[4]^2)^(5/2)*(-9*K[4] + Sqrt[-96*K[3]^3 + 81*K[4]^2])^(2/3)), {K[3], 1, x}])/(72*x*K[4]*(-32*x^3 + 27*K[4]^2)^(3/2)), {K[4], 1, y[x]}], y[x]], Solve[C[1] == Inactive[Integrate][(-27*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*y[x]^2*(-9*y[x] + Sqrt[-96*K[5]^3 + 81*y[x]^2])^(2/3) + 4*K[5]^2*(288*K[5]^2 + 2^(2/3)*3^(1/3)*(3*I + Sqrt[3])*Sqrt[-32*K[5]^3 + 27*y[x]^2]*(-9*y[x] + Sqrt[-96*K[5]^3 + 81*y[x]^2])^(1/3) - 4*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*K[5]*(-9*y[x] + Sqrt[-96*K[5]^3 + 81*y[x]^2])^(2/3)) + 9*y[x]*(12*2^(2/3)*3^(1/3)*(1 + I*Sqrt[3])*K[5]^2*(-9*y[x] + Sqrt[-96*K[5]^3 + 81*y[x]^2])^(1/3) + I*2^(1/3)*3^(1/6)*(I + Sqrt[3])*Sqrt[-32*K[5]^3 + 27*y[x]^2]*(-9*y[x] + Sqrt[-96*K[5]^3 + 81*y[x]^2])^(2/3)))/(48*K[5]^2*(32*K[5]^3 - 27*y[x]^2)), {K[5], 1, x}] + Inactive[Integrate][(-384*x^4*Sqrt[-32*x^3 + 27*K[6]^2] + 1296*x*K[6]^2*Sqrt[-32*x^3 + 27*K[6]^2] - 128*2^(2/3)*3^(1/3)*(3*I + Sqrt[3])*x^5*(-9*K[6] + Sqrt[-96*x^3 + 81*K[6]^2])^(1/3) + 108*2^(2/3)*3^(1/3)*x^2*K[6]*((3*I + Sqrt[3])*K[6] + (1 + I*Sqrt[3])*Sqrt[-32*x^3 + 27*K[6]^2])*(-9*K[6] + Sqrt[-96*x^3 + 81*K[6]^2])^(1/3) - 27*2^(1/3)*3^(1/6)*K[6]^2*((9 - (9*I)*Sqrt[3])*K[6] + (-3*I + Sqrt[3])*Sqrt[-32*x^3 + 27*K[6]^2])*(-9*K[6] + Sqrt[-96*x^3 + 81*K[6]^2])^(2/3) - 16*2^(1/3)*3^(1/6)*x^3*((18*I)*(I + Sqrt[3])*K[6] + (-3*I + Sqrt[3])*Sqrt[-32*x^3 + 27*K[6]^2])*(-9*K[6] + Sqrt[-96*x^3 + 81*K[6]^2])^(2/3) - 72*x*K[6]*(-32*x^3 + 27*K[6]^2)^(3/2)*Inactive[Integrate][(-2048*2^(2/3)*3^(1/3)*(3*I + Sqrt[3])*K[5]^6 + 243*2^(2/3)*3^(1/3)*K[6]^3*(3*(3*I + Sqrt[3])*K[6] + (-1 - I*Sqrt[3])*Sqrt[-32*K[5]^3 + 27*K[6]^2]) + 144*2^(2/3)*3^(1/3)*K[5]^3*K[6]*(6*(3*I + Sqrt[3])*K[6] - (7*I)*(-I + Sqrt[3])*Sqrt[-32*K[5]^3 + 27*K[6]^2]) + 64*2^(1/3)*3^(1/6)*K[5]^4*(27*(1 - I*Sqrt[3])*K[6] + 4*(-3*I + Sqrt[3])*Sqrt[-32*K[5]^3 + 27*K[6]^2])*(-9*K[6] + Sqrt[-96*K[5]^3 + 81*K[6]^2])^(1/3) + 54*2^(1/3)*3^(1/6)*K[5]*K[6]^2*((27*I)*(I + Sqrt[3])*K[6] + 5*(-3*I + Sqrt[3])*Sqrt[-32*K[5]^3 + 27*K[6]^2])*(-9*K[6] + Sqrt[-96*K[5]^3 + 81*K[6]^2])^(1/3) + 1296*K[5]^2*K[6]*Sqrt[-32*K[5]^3 + 27*K[6]^2]*(-9*K[6] + Sqrt[-96*K[5]^3 + 81*K[6]^2])^(2/3))/((-32*K[5]^3 + 27*K[6]^2)^(5/2)*(-9*K[6] + Sqrt[-96*K[5]^3 + 81*K[6]^2])^(2/3)), {K[5], 1, x}])/(72*x*K[6]*(-32*x^3 + 27*K[6]^2)^(3/2)), {K[6], 1, y[x]}], y[x]]}
Maple raw input
dsolve(diff(y(x),x)^3-2*x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[-_C1/(((108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)+24*x)/(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(1/3))^(2/3)+x-1/96*((108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)+24*x)^2/(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3) = 0, -_C1/((I*(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)*3^(1/2)-24*I*3^(1/2)*x-(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)-24*x)/(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(1/3))^(2/3)+x-1/384*(I*(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)*3^(1/2)-24*I*3^(1/2)*x-(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)-24*x)^2/(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3) = 0, -12^(2/3)/((-I*(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)*3^(1/2)+24*I*3^(1/2)*x-(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)-24*x)/(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(1/3))^(2/3)*_C1+x-1/384*(I*(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)*3^(1/2)-24*I*3^(1/2)*x+(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3)+24*x)^2/(108*y(x)+12*(-96*x^3+81*y(x)^2)^(1/2))^(2/3) = 0]