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 = 406.892 (sec), leaf count = 2930
\[\left \{\text {Solve}\left [c_1=\int _1^x\frac {-4 \left (-48 K[1]^2+4 \sqrt [3]{2} 3^{2/3} \left (\sqrt {96 K[1]^3+81 y(x)^2}-9 y(x)\right )^{2/3} K[1]+2^{2/3} 3^{5/6} \sqrt {32 K[1]^3+27 y(x)^2} \sqrt [3]{\sqrt {96 K[1]^3+81 y(x)^2}-9 y(x)}\right ) K[1]^2+9 y(x) \left (4\ 2^{2/3} \sqrt [3]{3} K[1]^2 \sqrt [3]{\sqrt {96 K[1]^3+81 y(x)^2}-9 y(x)}-\sqrt [3]{2} \sqrt [6]{3} \sqrt {32 K[1]^3+27 y(x)^2} \left (\sqrt {96 K[1]^3+81 y(x)^2}-9 y(x)\right )^{2/3}\right )-27 \sqrt [3]{2} 3^{2/3} y(x)^2 \left (\sqrt {96 K[1]^3+81 y(x)^2}-9 y(x)\right )^{2/3}}{384 K[1]^5+648 y(x)^2 K[1]^2}dK[1]+\int _1^{y(x)}\frac {192 x^4+16 \sqrt [3]{2} 3^{2/3} \left (\sqrt {96 x^3+81 K[2]^2}-9 K[2]\right )^{2/3} x^3+4\ 2^{2/3} \sqrt [3]{3} \left (\sqrt {96 x^3+81 K[2]^2}-9 K[2]\right )^{4/3} x^2+648 K[2]^2 x-36 \left (16 K[2] x^4+27 K[2]^3 x\right ) \int _1^x\frac {2 \left (512\ 2^{2/3} 3^{5/6} K[1]^6-64 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {96 K[1]^3+81 K[2]^2}-18 K[2]\right ) \sqrt [3]{\sqrt {96 K[1]^3+81 K[2]^2}-9 K[2]} K[1]^4-144\ 2^{2/3} \sqrt [3]{3} K[2] \left (6 \sqrt {3} K[2]-\sqrt {32 K[1]^3+27 K[2]^2}\right ) K[1]^3-216 K[2] \sqrt {32 K[1]^3+27 K[2]^2} \left (\sqrt {96 K[1]^3+81 K[2]^2}-9 K[2]\right )^{2/3} K[1]^2+54 \sqrt [3]{2} \sqrt [6]{3} K[2]^2 \sqrt [3]{\sqrt {96 K[1]^3+81 K[2]^2}-9 K[2]} \left (9 K[2]+\sqrt {96 K[1]^3+81 K[2]^2}\right ) K[1]+243\ 2^{2/3} \sqrt [3]{3} K[2]^3 \left (\sqrt {32 K[1]^3+27 K[2]^2}-3 \sqrt {3} K[2]\right )\right )}{\left (16 K[1]^3+27 K[2]^2\right )^2 \sqrt {32 K[1]^3+27 K[2]^2} \left (\sqrt {96 K[1]^3+81 K[2]^2}-9 K[2]\right )^{2/3}}dK[1]+9 \sqrt [3]{2} \sqrt [6]{3} K[2] \left (3 \sqrt {3} K[2]+\sqrt {32 x^3+27 K[2]^2}\right ) \left (\sqrt {96 x^3+81 K[2]^2}-9 K[2]\right )^{2/3}}{576 K[2] x^4+972 K[2]^3 x}dK[2],y(x)\right ],\text {Solve}\left [c_1=\int _1^x\frac {4 \left (96 K[3]^2+4 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) \left (\sqrt {96 K[3]^3+81 y(x)^2}-9 y(x)\right )^{2/3} K[3]+2^{2/3} \sqrt [3]{3} \left (-3 i+\sqrt {3}\right ) \sqrt {32 K[3]^3+27 y(x)^2} \sqrt [3]{\sqrt {96 K[3]^3+81 y(x)^2}-9 y(x)}\right ) K[3]^2+9 y(x) \left (4 i 2^{2/3} \sqrt [3]{3} \left (i+\sqrt {3}\right ) \sqrt [3]{\sqrt {96 K[3]^3+81 y(x)^2}-9 y(x)} K[3]^2+\sqrt [3]{2} \sqrt [6]{3} \left (1+i \sqrt {3}\right ) \sqrt {32 K[3]^3+27 y(x)^2} \left (\sqrt {96 K[3]^3+81 y(x)^2}-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 {96 K[3]^3+81 y(x)^2}-9 y(x)\right )^{2/3}}{48 K[3]^2 \left (16 K[3]^3+27 y(x)^2\right )}dK[3]+\int _1^{y(x)}-\frac {-384 x^4+16 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) \left (\sqrt {96 x^3+81 K[4]^2}-9 K[4]\right )^{2/3} x^3+4\ 2^{2/3} \sqrt [3]{3} \left (9 i \left (i+\sqrt {3}\right ) K[4]+\left (-3 i+\sqrt {3}\right ) \sqrt {32 x^3+27 K[4]^2}\right ) \sqrt [3]{\sqrt {96 x^3+81 K[4]^2}-9 K[4]} x^2-1296 K[4]^2 x+72 \left (16 K[4] x^4+27 K[4]^3 x\right ) \int _1^x\frac {-512 2^{2/3} \sqrt [3]{3} \left (-3 i+\sqrt {3}\right ) K[3]^6+64 \sqrt [3]{2} \sqrt [6]{3} \left (\left (3 i+\sqrt {3}\right ) \sqrt {32 K[3]^3+27 K[4]^2}-18 i \left (-i+\sqrt {3}\right ) K[4]\right ) \sqrt [3]{\sqrt {96 K[3]^3+81 K[4]^2}-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]+i \left (i+\sqrt {3}\right ) \sqrt {32 K[3]^3+27 K[4]^2}\right ) K[3]^3-432 K[4] \sqrt {32 K[3]^3+27 K[4]^2} \left (\sqrt {96 K[3]^3+81 K[4]^2}-9 K[4]\right )^{2/3} K[3]^2-54 \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 {32 K[3]^3+27 K[4]^2}\right ) \sqrt [3]{\sqrt {96 K[3]^3+81 K[4]^2}-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 {32 K[3]^3+27 K[4]^2}\right )}{\left (16 K[3]^3+27 K[4]^2\right )^2 \sqrt {32 K[3]^3+27 K[4]^2} \left (\sqrt {96 K[3]^3+81 K[4]^2}-9 K[4]\right )^{2/3}}dK[3]+9 i \sqrt [3]{2} \sqrt [6]{3} K[4] \left (\left (9-3 i \sqrt {3}\right ) K[4]+\left (-i+\sqrt {3}\right ) \sqrt {32 x^3+27 K[4]^2}\right ) \left (\sqrt {96 x^3+81 K[4]^2}-9 K[4]\right )^{2/3}}{72 \left (16 K[4] x^4+27 K[4]^3 x\right )}dK[4],y(x)\right ],\text {Solve}\left [c_1=\int _1^x\frac {4 \left (96 K[5]^2+4 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) \left (\sqrt {96 K[5]^3+81 y(x)^2}-9 y(x)\right )^{2/3} K[5]+2^{2/3} \sqrt [3]{3} \left (3 i+\sqrt {3}\right ) \sqrt {32 K[5]^3+27 y(x)^2} \sqrt [3]{\sqrt {96 K[5]^3+81 y(x)^2}-9 y(x)}\right ) K[5]^2+9 y(x) \left (\sqrt [3]{2} \sqrt [6]{3} \left (1-i \sqrt {3}\right ) \sqrt {32 K[5]^3+27 y(x)^2} \left (\sqrt {96 K[5]^3+81 y(x)^2}-9 y(x)\right )^{2/3}-4 i 2^{2/3} \sqrt [3]{3} \left (-i+\sqrt {3}\right ) K[5]^2 \sqrt [3]{\sqrt {96 K[5]^3+81 y(x)^2}-9 y(x)}\right )+27 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) y(x)^2 \left (\sqrt {96 K[5]^3+81 y(x)^2}-9 y(x)\right )^{2/3}}{48 K[5]^2 \left (16 K[5]^3+27 y(x)^2\right )}dK[5]+\int _1^{y(x)}\frac {384 x^4-16 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) \left (\sqrt {96 x^3+81 K[6]^2}-9 K[6]\right )^{2/3} x^3-4\ 2^{2/3} \sqrt [3]{3} \left (\left (-9-9 i \sqrt {3}\right ) K[6]+\left (3 i+\sqrt {3}\right ) \sqrt {32 x^3+27 K[6]^2}\right ) \sqrt [3]{\sqrt {96 x^3+81 K[6]^2}-9 K[6]} x^2+1296 K[6]^2 x-72 \left (16 K[6] x^4+27 K[6]^3 x\right ) \int _1^x\frac {-512 2^{2/3} \sqrt [3]{3} \left (3 i+\sqrt {3}\right ) K[5]^6+64 \sqrt [3]{2} \sqrt [6]{3} \left (18 i \left (i+\sqrt {3}\right ) K[6]+\left (-3 i+\sqrt {3}\right ) \sqrt {32 K[5]^3+27 K[6]^2}\right ) \sqrt [3]{\sqrt {96 K[5]^3+81 K[6]^2}-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]+\left (-1-i \sqrt {3}\right ) \sqrt {32 K[5]^3+27 K[6]^2}\right ) K[5]^3-432 K[6] \sqrt {32 K[5]^3+27 K[6]^2} \left (\sqrt {96 K[5]^3+81 K[6]^2}-9 K[6]\right )^{2/3} K[5]^2-54 \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 {32 K[5]^3+27 K[6]^2}\right ) \sqrt [3]{\sqrt {96 K[5]^3+81 K[6]^2}-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 {32 K[5]^3+27 K[6]^2}\right )}{\left (16 K[5]^3+27 K[6]^2\right )^2 \sqrt {32 K[5]^3+27 K[6]^2} \left (\sqrt {96 K[5]^3+81 K[6]^2}-9 K[6]\right )^{2/3}}dK[5]+9 i \sqrt [3]{2} \sqrt [6]{3} K[6] \left (\left (9+3 i \sqrt {3}\right ) K[6]+\left (i+\sqrt {3}\right ) \sqrt {32 x^3+27 K[6]^2}\right ) \left (\sqrt {96 x^3+81 K[6]^2}-9 K[6]\right )^{2/3}}{72 \left (16 K[6] x^4+27 K[6]^3 x\right )}dK[6],y(x)\right ]\right \}\]
Maple ✓
cpu = 0.234 (sec), leaf count = 173
\[\left [y \left (x \right ) = -\frac {\left (-6 \sqrt {x^{2}+3 \textit {\_C1}}-6 x \right )^{\frac {3}{2}}}{27}-\frac {2 x \sqrt {-6 \sqrt {x^{2}+3 \textit {\_C1}}-6 x}}{3}, y \left (x \right ) = \frac {\left (-6 \sqrt {x^{2}+3 \textit {\_C1}}-6 x \right )^{\frac {3}{2}}}{27}+\frac {2 x \sqrt {-6 \sqrt {x^{2}+3 \textit {\_C1}}-6 x}}{3}, y \left (x \right ) = -\frac {\left (6 \sqrt {x^{2}+3 \textit {\_C1}}-6 x \right )^{\frac {3}{2}}}{27}-\frac {2 x \sqrt {6 \sqrt {x^{2}+3 \textit {\_C1}}-6 x}}{3}, y \left (x \right ) = \frac {\left (6 \sqrt {x^{2}+3 \textit {\_C1}}-6 x \right )^{\frac {3}{2}}}{27}+\frac {2 x \sqrt {6 \sqrt {x^{2}+3 \textit {\_C1}}-6 x}}{3}\right ]\] 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*(-48*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)) + 9*y[x]*(4*2^(2/3)*3^(1/3)*K[1]^2*(-9*y[x] + Sqrt[96*K[1]^3 + 81*y[x]^2])^(1/3) - 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)))/(384*K[1]^5 + 648*K[1]^2*y[x]^2), {K[1], 1, x}] + Inactive[Integrate][(192*x^4 + 648*x*K[2]^2 + 16*2^(1/3)*3^(2/3)*x^3*(-9*K[2] + Sqrt[96*x^3 + 81*K[2]^2])^(2/3) + 9*2^(1/3)*3^(1/6)*K[2]*(3*Sqrt[3]*K[2] + Sqrt[32*x^3 + 27*K[2]^2])*(-9*K[2] + Sqrt[96*x^3 + 81*K[2]^2])^(2/3) + 4*2^(2/3)*3^(1/3)*x^2*(-9*K[2] + Sqrt[96*x^3 + 81*K[2]^2])^(4/3) - 36*(16*x^4*K[2] + 27*x*K[2]^3)*Inactive[Integrate][(2*(512*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] - 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]) - 64*2^(1/3)*3^(1/6)*K[1]^4*(-18*K[2] + Sqrt[96*K[1]^3 + 81*K[2]^2])*(-9*K[2] + Sqrt[96*K[1]^3 + 81*K[2]^2])^(1/3) - 216*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) + 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)*(9*K[2] + Sqrt[96*K[1]^3 + 81*K[2]^2])))/((16*K[1]^3 + 27*K[2]^2)^2*Sqrt[32*K[1]^3 + 27*K[2]^2]*(-9*K[2] + Sqrt[96*K[1]^3 + 81*K[2]^2])^(2/3)), {K[1], 1, x}])/(576*x^4*K[2] + 972*x*K[2]^3), {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*(96*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]*((4*I)*2^(2/3)*3^(1/3)*(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*(16*K[3]^3 + 27*y[x]^2)), {K[3], 1, x}] + Inactive[Integrate][-1/72*(-384*x^4 - 1296*x*K[4]^2 + 4*2^(2/3)*3^(1/3)*x^2*((9*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])^(1/3) + 16*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*x^3*(-9*K[4] + Sqrt[96*x^3 + 81*K[4]^2])^(2/3) + (9*I)*2^(1/3)*3^(1/6)*K[4]*((9 - (3*I)*Sqrt[3])*K[4] + (-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*(16*x^4*K[4] + 27*x*K[4]^3)*Inactive[Integrate][(-512*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] + I*(I + Sqrt[3])*Sqrt[32*K[3]^3 + 27*K[4]^2]) - 54*2^(1/3)*3^(1/6)*K[3]*K[4]^2*((9 + (9*I)*Sqrt[3])*K[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) + 64*2^(1/3)*3^(1/6)*K[3]^4*((-18*I)*(-I + Sqrt[3])*K[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) - 432*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))/((16*K[3]^3 + 27*K[4]^2)^2*Sqrt[32*K[3]^3 + 27*K[4]^2]*(-9*K[4] + Sqrt[96*K[3]^3 + 81*K[4]^2])^(2/3)), {K[3], 1, x}])/(16*x^4*K[4] + 27*x*K[4]^3), {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*(96*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]*((-4*I)*2^(2/3)*3^(1/3)*(-I + Sqrt[3])*K[5]^2*(-9*y[x] + Sqrt[96*K[5]^3 + 81*y[x]^2])^(1/3) + 2^(1/3)*3^(1/6)*(1 - 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*(16*K[5]^3 + 27*y[x]^2)), {K[5], 1, x}] + Inactive[Integrate][(384*x^4 + 1296*x*K[6]^2 - 4*2^(2/3)*3^(1/3)*x^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])^(1/3) - 16*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*x^3*(-9*K[6] + Sqrt[96*x^3 + 81*K[6]^2])^(2/3) + (9*I)*2^(1/3)*3^(1/6)*K[6]*((9 + (3*I)*Sqrt[3])*K[6] + (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*(16*x^4*K[6] + 27*x*K[6]^3)*Inactive[Integrate][(-512*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] + (-1 - I*Sqrt[3])*Sqrt[32*K[5]^3 + 27*K[6]^2]) - 54*2^(1/3)*3^(1/6)*K[5]*K[6]^2*((9 - (9*I)*Sqrt[3])*K[6] + (-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) + 64*2^(1/3)*3^(1/6)*K[5]^4*((18*I)*(I + Sqrt[3])*K[6] + (-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) - 432*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))/((16*K[5]^3 + 27*K[6]^2)^2*Sqrt[32*K[5]^3 + 27*K[6]^2]*(-9*K[6] + Sqrt[96*K[5]^3 + 81*K[6]^2])^(2/3)), {K[5], 1, x}])/(72*(16*x^4*K[6] + 27*x*K[6]^3)), {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
[y(x) = -1/27*(-6*(x^2+3*_C1)^(1/2)-6*x)^(3/2)-2/3*x*(-6*(x^2+3*_C1)^(1/2)-6*x)^(1/2), y(x) = 1/27*(-6*(x^2+3*_C1)^(1/2)-6*x)^(3/2)+2/3*x*(-6*(x^2+3*_C1)^(1/2)-6*x)^(1/2), y(x) = -1/27*(6*(x^2+3*_C1)^(1/2)-6*x)^(3/2)-2/3*x*(6*(x^2+3*_C1)^(1/2)-6*x)^(1/2), y(x) = 1/27*(6*(x^2+3*_C1)^(1/2)-6*x)^(3/2)+2/3*x*(6*(x^2+3*_C1)^(1/2)-6*x)^(1/2)]