ODE
\[ x^6 y'(x)^3-x y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 382.987 (sec), leaf count = 2841
\[\left \{\text {Solve}\left [c_1=\int _1^x\frac {27 \sqrt {3} y(x)^2 \left (\sqrt {3} \sqrt {K[1]^{21} \left (27 K[1]^3 y(x)^2-4\right )}-9 K[1]^{12} y(x)\right )^{2/3} K[1]^{12}-4 \sqrt {3} \left (\sqrt {3} \sqrt {K[1]^{21} \left (27 K[1]^3 y(x)^2-4\right )}-9 K[1]^{12} y(x)\right )^{2/3} K[1]^9+2\ 3^{2/3} \sqrt {K[1]^{21} \left (27 K[1]^3 y(x)^2-4\right )} \sqrt [3]{2 \sqrt {3} \sqrt {K[1]^{21} \left (27 K[1]^3 y(x)^2-4\right )}-18 K[1]^{12} y(x)} K[1]^2+9 y(x) \sqrt {K[1]^{21} \left (27 K[1]^3 y(x)^2-4\right )} \left (\sqrt {3} \sqrt {K[1]^{21} \left (27 K[1]^3 y(x)^2-4\right )}-9 K[1]^{12} y(x)\right )^{2/3}}{2^{2/3} 3^{5/6} K[1]^{17} \left (27 K[1]^3 y(x)^2-4\right )}dK[1]+\int _1^{y(x)}\frac {-162 K[2]^2 x^{19}-9 K[2] \left (27 x^3 K[2]^2-4\right ) \int _1^x\frac {2 \sqrt [3]{2} \sqrt [6]{3} K[1]^{25} \left (27 \sqrt [3]{2} 3^{2/3} K[2]^2 K[1]^{17}+2 \sqrt [3]{2} 3^{2/3} K[1]^{14}+27 K[2] \sqrt [3]{\sqrt {3} \sqrt {K[1]^{21} \left (27 K[1]^3 K[2]^2-4\right )}-9 K[1]^{12} K[2]} K[1]^{12}-9 \sqrt [3]{2} \sqrt [6]{3} K[2] \sqrt {K[1]^{21} \left (27 K[1]^3 K[2]^2-4\right )} K[1]^5-\sqrt {3} \sqrt {K[1]^{21} \left (27 K[1]^3 K[2]^2-4\right )} \sqrt [3]{\sqrt {3} \sqrt {K[1]^{21} \left (27 K[1]^3 K[2]^2-4\right )}-9 K[1]^{12} K[2]}\right )}{\left (K[1]^{21} \left (27 K[1]^3 K[2]^2-4\right )\right )^{3/2} \left (\sqrt {3} \sqrt {K[1]^{21} \left (27 K[1]^3 K[2]^2-4\right )}-9 K[1]^{12} K[2]\right )^{2/3}}dK[1] x^{16}+24 x^{16}+27 \sqrt [3]{2} K[2]^2 \left (3 \sqrt {3} \sqrt {x^{21} \left (27 x^3 K[2]^2-4\right )}-27 x^{12} K[2]\right )^{2/3} x^{12}-4 \sqrt [3]{2} \left (3 \sqrt {3} \sqrt {x^{21} \left (27 x^3 K[2]^2-4\right )}-27 x^{12} K[2]\right )^{2/3} x^9+2\ 2^{2/3} 3^{5/6} \sqrt {x^{21} \left (27 x^3 K[2]^2-4\right )} \sqrt [3]{\sqrt {3} \sqrt {x^{21} \left (27 x^3 K[2]^2-4\right )}-9 x^{12} K[2]} x^2+9 \sqrt [3]{2} \sqrt [6]{3} K[2] \sqrt {x^{21} \left (27 x^3 K[2]^2-4\right )} \left (\sqrt {3} \sqrt {x^{21} \left (27 x^3 K[2]^2-4\right )}-9 x^{12} K[2]\right )^{2/3}}{9 x^{16} K[2] \left (27 x^3 K[2]^2-4\right )}dK[2],y(x)\right ],\text {Solve}\left [c_1=\int _1^x-\frac {\sqrt [3]{2 \sqrt {3} \sqrt {K[3]^{21} \left (27 K[3]^3 y(x)^2-4\right )}-18 K[3]^{12} y(x)} \left (27 \left (3 i+\sqrt {3}\right ) y(x)^2 \sqrt [3]{\sqrt {3} \sqrt {K[3]^{21} \left (27 K[3]^3 y(x)^2-4\right )}-9 K[3]^{12} y(x)} K[3]^{12}-4 \left (3 i+\sqrt {3}\right ) \sqrt [3]{\sqrt {3} \sqrt {K[3]^{21} \left (27 K[3]^3 y(x)^2-4\right )}-9 K[3]^{12} y(x)} K[3]^9+2 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) \sqrt {K[3]^{21} \left (27 K[3]^3 y(x)^2-4\right )} K[3]^2+9 \left (1+i \sqrt {3}\right ) y(x) \sqrt {K[3]^{21} \left (27 K[3]^3 y(x)^2-4\right )} \sqrt [3]{\sqrt {3} \sqrt {K[3]^{21} \left (27 K[3]^3 y(x)^2-4\right )}-9 K[3]^{12} y(x)}\right )}{4\ 3^{5/6} K[3]^{17} \left (27 K[3]^3 y(x)^2-4\right )}dK[3]+\int _1^{y(x)}\frac {-324 K[4]^2 x^{19}+18 K[4] \left (4-27 x^3 K[4]^2\right ) \int _1^x\frac {\sqrt [3]{2} \sqrt [6]{3} K[3]^{25} \left (-27 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) K[4]^2 K[3]^{17}-2 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) K[3]^{14}-27 i \left (-i+\sqrt {3}\right ) K[4] \sqrt [3]{\sqrt {3} \sqrt {K[3]^{21} \left (27 K[3]^3 K[4]^2-4\right )}-9 K[3]^{12} K[4]} K[3]^{12}+9 \sqrt [3]{2} \sqrt [6]{3} \left (1-i \sqrt {3}\right ) K[4] \sqrt {K[3]^{21} \left (27 K[3]^3 K[4]^2-4\right )} K[3]^5+\left (3 i+\sqrt {3}\right ) \sqrt {K[3]^{21} \left (27 K[3]^3 K[4]^2-4\right )} \sqrt [3]{\sqrt {3} \sqrt {K[3]^{21} \left (27 K[3]^3 K[4]^2-4\right )}-9 K[3]^{12} K[4]}\right )}{\left (K[3]^{21} \left (27 K[3]^3 K[4]^2-4\right )\right )^{3/2} \left (\sqrt {3} \sqrt {K[3]^{21} \left (27 K[3]^3 K[4]^2-4\right )}-9 K[3]^{12} K[4]\right )^{2/3}}dK[3] x^{16}+48 x^{16}-27 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) K[4]^2 \left (\sqrt {3} \sqrt {x^{21} \left (27 x^3 K[4]^2-4\right )}-9 x^{12} K[4]\right )^{2/3} x^{12}+4 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) \left (\sqrt {3} \sqrt {x^{21} \left (27 x^3 K[4]^2-4\right )}-9 x^{12} K[4]\right )^{2/3} x^9-2\ 2^{2/3} \left (-3 i+\sqrt {3}\right ) \sqrt {x^{21} \left (27 x^3 K[4]^2-4\right )} \sqrt [3]{3 \sqrt {3} \sqrt {x^{21} \left (27 x^3 K[4]^2-4\right )}-27 x^{12} K[4]} x^2-9 i \sqrt [3]{2} \sqrt [6]{3} \left (-i+\sqrt {3}\right ) K[4] \sqrt {x^{21} \left (27 x^3 K[4]^2-4\right )} \left (\sqrt {3} \sqrt {x^{21} \left (27 x^3 K[4]^2-4\right )}-9 x^{12} K[4]\right )^{2/3}}{18 x^{16} K[4] \left (27 x^3 K[4]^2-4\right )}dK[4],y(x)\right ],\text {Solve}\left [c_1=\int _1^x-\frac {\sqrt [3]{2 \sqrt {3} \sqrt {K[5]^{21} \left (27 K[5]^3 y(x)^2-4\right )}-18 K[5]^{12} y(x)} \left (27 \left (-3 i+\sqrt {3}\right ) y(x)^2 \sqrt [3]{\sqrt {3} \sqrt {K[5]^{21} \left (27 K[5]^3 y(x)^2-4\right )}-9 K[5]^{12} y(x)} K[5]^{12}-4 \left (-3 i+\sqrt {3}\right ) \sqrt [3]{\sqrt {3} \sqrt {K[5]^{21} \left (27 K[5]^3 y(x)^2-4\right )}-9 K[5]^{12} y(x)} K[5]^9+2 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) \sqrt {K[5]^{21} \left (27 K[5]^3 y(x)^2-4\right )} K[5]^2+9 \left (1-i \sqrt {3}\right ) y(x) \sqrt {K[5]^{21} \left (27 K[5]^3 y(x)^2-4\right )} \sqrt [3]{\sqrt {3} \sqrt {K[5]^{21} \left (27 K[5]^3 y(x)^2-4\right )}-9 K[5]^{12} y(x)}\right )}{4\ 3^{5/6} K[5]^{17} \left (27 K[5]^3 y(x)^2-4\right )}dK[5]+\int _1^{y(x)}\frac {-324 K[6]^2 x^{19}+18 K[6] \left (4-27 x^3 K[6]^2\right ) \int _1^x\frac {\sqrt [3]{2} \sqrt [6]{3} K[5]^{25} \left (-27 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) K[6]^2 K[5]^{17}-2 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) K[5]^{14}+27 i \left (i+\sqrt {3}\right ) K[6] \sqrt [3]{\sqrt {3} \sqrt {K[5]^{21} \left (27 K[5]^3 K[6]^2-4\right )}-9 K[5]^{12} K[6]} K[5]^{12}+9 \sqrt [3]{2} \sqrt [6]{3} \left (1+i \sqrt {3}\right ) K[6] \sqrt {K[5]^{21} \left (27 K[5]^3 K[6]^2-4\right )} K[5]^5+\left (-3 i+\sqrt {3}\right ) \sqrt {K[5]^{21} \left (27 K[5]^3 K[6]^2-4\right )} \sqrt [3]{\sqrt {3} \sqrt {K[5]^{21} \left (27 K[5]^3 K[6]^2-4\right )}-9 K[5]^{12} K[6]}\right )}{\left (K[5]^{21} \left (27 K[5]^3 K[6]^2-4\right )\right )^{3/2} \left (\sqrt {3} \sqrt {K[5]^{21} \left (27 K[5]^3 K[6]^2-4\right )}-9 K[5]^{12} K[6]\right )^{2/3}}dK[5] x^{16}+48 x^{16}-27 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) K[6]^2 \left (\sqrt {3} \sqrt {x^{21} \left (27 x^3 K[6]^2-4\right )}-9 x^{12} K[6]\right )^{2/3} x^{12}+4 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) \left (\sqrt {3} \sqrt {x^{21} \left (27 x^3 K[6]^2-4\right )}-9 x^{12} K[6]\right )^{2/3} x^9-2\ 2^{2/3} \left (3 i+\sqrt {3}\right ) \sqrt {x^{21} \left (27 x^3 K[6]^2-4\right )} \sqrt [3]{3 \sqrt {3} \sqrt {x^{21} \left (27 x^3 K[6]^2-4\right )}-27 x^{12} K[6]} x^2+9 i \sqrt [3]{2} \sqrt [6]{3} \left (i+\sqrt {3}\right ) K[6] \sqrt {x^{21} \left (27 x^3 K[6]^2-4\right )} \left (\sqrt {3} \sqrt {x^{21} \left (27 x^3 K[6]^2-4\right )}-9 x^{12} K[6]\right )^{2/3}}{18 x^{16} K[6] \left (27 x^3 K[6]^2-4\right )}dK[6],y(x)\right ]\right \}\]
Maple ✓
cpu = 1.713 (sec), leaf count = 42
\[\left [y \left (x \right ) = -\frac {2 \sqrt {3}}{9 x^{\frac {3}{2}}}, y \left (x \right ) = \frac {2 \sqrt {3}}{9 x^{\frac {3}{2}}}, y \left (x \right ) = \textit {\_C1}^{6}-\sqrt {\frac {\textit {\_C1}^{2}}{x^{2}}}\, \textit {\_C1}\right ]\] Mathematica raw input
DSolve[-y[x] - x*y'[x] + x^6*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{Solve[C[1] == Inactive[Integrate][(-4*Sqrt[3]*K[1]^9*(-9*K[1]^12*y[x] + Sqrt[3]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*y[x]^2)])^(2/3) + 27*Sqrt[3]*K[1]^12*y[x]^2*(-9*K[1]^12*y[x] + Sqrt[3]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*y[x]^2)])^(2/3) + 9*y[x]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*y[x]^2)]*(-9*K[1]^12*y[x] + Sqrt[3]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*y[x]^2)])^(2/3) + 2*3^(2/3)*K[1]^2*Sqrt[K[1]^21*(-4 + 27*K[1]^3*y[x]^2)]*(-18*K[1]^12*y[x] + 2*Sqrt[3]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*y[x]^2)])^(1/3))/(2^(2/3)*3^(5/6)*K[1]^17*(-4 + 27*K[1]^3*y[x]^2)), {K[1], 1, x}] + Inactive[Integrate][(24*x^16 - 162*x^19*K[2]^2 + 2*2^(2/3)*3^(5/6)*x^2*Sqrt[x^21*(-4 + 27*x^3*K[2]^2)]*(-9*x^12*K[2] + Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[2]^2)])^(1/3) + 9*2^(1/3)*3^(1/6)*K[2]*Sqrt[x^21*(-4 + 27*x^3*K[2]^2)]*(-9*x^12*K[2] + Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[2]^2)])^(2/3) - 4*2^(1/3)*x^9*(-27*x^12*K[2] + 3*Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[2]^2)])^(2/3) + 27*2^(1/3)*x^12*K[2]^2*(-27*x^12*K[2] + 3*Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[2]^2)])^(2/3) - 9*x^16*K[2]*(-4 + 27*x^3*K[2]^2)*Inactive[Integrate][(2*2^(1/3)*3^(1/6)*K[1]^25*(2*2^(1/3)*3^(2/3)*K[1]^14 + 27*2^(1/3)*3^(2/3)*K[1]^17*K[2]^2 - 9*2^(1/3)*3^(1/6)*K[1]^5*K[2]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*K[2]^2)] + 27*K[1]^12*K[2]*(-9*K[1]^12*K[2] + Sqrt[3]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*K[2]^2)])^(1/3) - Sqrt[3]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*K[2]^2)]*(-9*K[1]^12*K[2] + Sqrt[3]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*K[2]^2)])^(1/3)))/((K[1]^21*(-4 + 27*K[1]^3*K[2]^2))^(3/2)*(-9*K[1]^12*K[2] + Sqrt[3]*Sqrt[K[1]^21*(-4 + 27*K[1]^3*K[2]^2)])^(2/3)), {K[1], 1, x}])/(9*x^16*K[2]*(-4 + 27*x^3*K[2]^2)), {K[2], 1, y[x]}], y[x]], Solve[C[1] == Inactive[Integrate][-1/4*((-18*K[3]^12*y[x] + 2*Sqrt[3]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*y[x]^2)])^(1/3)*(2*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*K[3]^2*Sqrt[K[3]^21*(-4 + 27*K[3]^3*y[x]^2)] - 4*(3*I + Sqrt[3])*K[3]^9*(-9*K[3]^12*y[x] + Sqrt[3]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*y[x]^2)])^(1/3) + 27*(3*I + Sqrt[3])*K[3]^12*y[x]^2*(-9*K[3]^12*y[x] + Sqrt[3]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*y[x]^2)])^(1/3) + 9*(1 + I*Sqrt[3])*y[x]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*y[x]^2)]*(-9*K[3]^12*y[x] + Sqrt[3]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*y[x]^2)])^(1/3)))/(3^(5/6)*K[3]^17*(-4 + 27*K[3]^3*y[x]^2)), {K[3], 1, x}] + Inactive[Integrate][(48*x^16 - 324*x^19*K[4]^2 + 4*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*x^9*(-9*x^12*K[4] + Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[4]^2)])^(2/3) - 27*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*x^12*K[4]^2*(-9*x^12*K[4] + Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[4]^2)])^(2/3) - (9*I)*2^(1/3)*3^(1/6)*(-I + Sqrt[3])*K[4]*Sqrt[x^21*(-4 + 27*x^3*K[4]^2)]*(-9*x^12*K[4] + Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[4]^2)])^(2/3) - 2*2^(2/3)*(-3*I + Sqrt[3])*x^2*Sqrt[x^21*(-4 + 27*x^3*K[4]^2)]*(-27*x^12*K[4] + 3*Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[4]^2)])^(1/3) + 18*x^16*K[4]*(4 - 27*x^3*K[4]^2)*Inactive[Integrate][(2^(1/3)*3^(1/6)*K[3]^25*(-2*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*K[3]^14 - 27*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*K[3]^17*K[4]^2 + 9*2^(1/3)*3^(1/6)*(1 - I*Sqrt[3])*K[3]^5*K[4]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*K[4]^2)] - (27*I)*(-I + Sqrt[3])*K[3]^12*K[4]*(-9*K[3]^12*K[4] + Sqrt[3]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*K[4]^2)])^(1/3) + (3*I + Sqrt[3])*Sqrt[K[3]^21*(-4 + 27*K[3]^3*K[4]^2)]*(-9*K[3]^12*K[4] + Sqrt[3]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*K[4]^2)])^(1/3)))/((K[3]^21*(-4 + 27*K[3]^3*K[4]^2))^(3/2)*(-9*K[3]^12*K[4] + Sqrt[3]*Sqrt[K[3]^21*(-4 + 27*K[3]^3*K[4]^2)])^(2/3)), {K[3], 1, x}])/(18*x^16*K[4]*(-4 + 27*x^3*K[4]^2)), {K[4], 1, y[x]}], y[x]], Solve[C[1] == Inactive[Integrate][-1/4*((-18*K[5]^12*y[x] + 2*Sqrt[3]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*y[x]^2)])^(1/3)*(2*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*K[5]^2*Sqrt[K[5]^21*(-4 + 27*K[5]^3*y[x]^2)] - 4*(-3*I + Sqrt[3])*K[5]^9*(-9*K[5]^12*y[x] + Sqrt[3]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*y[x]^2)])^(1/3) + 27*(-3*I + Sqrt[3])*K[5]^12*y[x]^2*(-9*K[5]^12*y[x] + Sqrt[3]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*y[x]^2)])^(1/3) + 9*(1 - I*Sqrt[3])*y[x]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*y[x]^2)]*(-9*K[5]^12*y[x] + Sqrt[3]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*y[x]^2)])^(1/3)))/(3^(5/6)*K[5]^17*(-4 + 27*K[5]^3*y[x]^2)), {K[5], 1, x}] + Inactive[Integrate][(48*x^16 - 324*x^19*K[6]^2 + 4*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*x^9*(-9*x^12*K[6] + Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[6]^2)])^(2/3) - 27*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*x^12*K[6]^2*(-9*x^12*K[6] + Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[6]^2)])^(2/3) + (9*I)*2^(1/3)*3^(1/6)*(I + Sqrt[3])*K[6]*Sqrt[x^21*(-4 + 27*x^3*K[6]^2)]*(-9*x^12*K[6] + Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[6]^2)])^(2/3) - 2*2^(2/3)*(3*I + Sqrt[3])*x^2*Sqrt[x^21*(-4 + 27*x^3*K[6]^2)]*(-27*x^12*K[6] + 3*Sqrt[3]*Sqrt[x^21*(-4 + 27*x^3*K[6]^2)])^(1/3) + 18*x^16*K[6]*(4 - 27*x^3*K[6]^2)*Inactive[Integrate][(2^(1/3)*3^(1/6)*K[5]^25*(-2*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*K[5]^14 - 27*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*K[5]^17*K[6]^2 + 9*2^(1/3)*3^(1/6)*(1 + I*Sqrt[3])*K[5]^5*K[6]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*K[6]^2)] + (27*I)*(I + Sqrt[3])*K[5]^12*K[6]*(-9*K[5]^12*K[6] + Sqrt[3]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*K[6]^2)])^(1/3) + (-3*I + Sqrt[3])*Sqrt[K[5]^21*(-4 + 27*K[5]^3*K[6]^2)]*(-9*K[5]^12*K[6] + Sqrt[3]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*K[6]^2)])^(1/3)))/((K[5]^21*(-4 + 27*K[5]^3*K[6]^2))^(3/2)*(-9*K[5]^12*K[6] + Sqrt[3]*Sqrt[K[5]^21*(-4 + 27*K[5]^3*K[6]^2)])^(2/3)), {K[5], 1, x}])/(18*x^16*K[6]*(-4 + 27*x^3*K[6]^2)), {K[6], 1, y[x]}], y[x]]}
Maple raw input
dsolve(x^6*diff(y(x),x)^3-x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = -2/9*3^(1/2)/x^(3/2), y(x) = 2/9*3^(1/2)/x^(3/2), y(x) = _C1^6-(1/x^2*_C1^2)^(1/2)*_C1]