ODE
\[ a y(x)+y'(x)^3-x y'(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 439.364 (sec), leaf count = 3587
\[\left \{\text {Solve}\left [c_1=\int _1^x\frac {2 \left (24 (a-1) K[1]^2-2 \sqrt [3]{2} 3^{2/3} \left (\sqrt {81 a^2 y(x)^2-12 K[1]^3}-9 a y(x)\right )^{2/3} K[1]+2^{2/3} 3^{5/6} \sqrt {27 a^2 y(x)^2-4 K[1]^3} \sqrt [3]{\sqrt {81 a^2 y(x)^2-12 K[1]^3}-9 a y(x)}\right ) K[1]^2+9 y(x) \left (2\ 2^{2/3} \sqrt [3]{3} (a-1) \sqrt [3]{\sqrt {81 a^2 y(x)^2-12 K[1]^3}-9 a y(x)} K[1]^2+\sqrt [3]{2} \sqrt [6]{3} \sqrt {27 a^2 y(x)^2-4 K[1]^3} \left (\sqrt {81 a^2 y(x)^2-12 K[1]^3}-9 a y(x)\right )^{2/3}\right )+27 \sqrt [3]{2} 3^{2/3} a y(x)^2 \left (\sqrt {81 a^2 y(x)^2-12 K[1]^3}-9 a y(x)\right )^{2/3}}{6 K[1]^2 \left (4 (2 a-3) K[1]^3+27 y(x)^2\right )}dK[1]+\int _1^{y(x)}-\frac {24 x^4-4 \sqrt [3]{2} 3^{2/3} \left (\sqrt {81 a^2 K[2]^2-12 x^3}-9 a K[2]\right )^{2/3} x^3+2\ 2^{2/3} \sqrt [3]{3} \left (9 (a-1) K[2]+\sqrt {81 a^2 K[2]^2-12 x^3}\right ) \sqrt [3]{\sqrt {81 a^2 K[2]^2-12 x^3}-9 a K[2]} x^2-162 K[2]^2 x+9 \left (4 (2 a-3) K[2] x^4+27 K[2]^3 x\right ) \int _1^x-\frac {2 \left (8\ 2^{2/3} 3^{5/6} (3-2 a)^2 K[1]^6-4 \sqrt [3]{2} \sqrt [6]{3} \sqrt [3]{\sqrt {81 a^2 K[2]^2-12 K[1]^3}-9 a K[2]} \left ((3-2 a)^2 \sqrt {81 a^2 K[2]^2-12 K[1]^3}-9 \left (4 a^3-4 a^2-3 a+6\right ) K[2]\right ) K[1]^4+18\ 2^{2/3} \sqrt [3]{3} K[2] \left (3 \sqrt {3} \left (8 a^3-12 a^2+2 a+3\right ) K[2]-2 \left (4 a^2-6 a+3\right ) \sqrt {27 a^2 K[2]^2-4 K[1]^3}\right ) K[1]^3+216 (a-1) K[2] \sqrt {27 a^2 K[2]^2-4 K[1]^3} \left (\sqrt {81 a^2 K[2]^2-12 K[1]^3}-9 a K[2]\right )^{2/3} K[1]^2+27 \sqrt [3]{2} \sqrt [6]{3} K[2]^2 \sqrt [3]{\sqrt {81 a^2 K[2]^2-12 K[1]^3}-9 a K[2]} \left (-36 K[2] a^2+9 K[2] a+4 \sqrt {81 a^2 K[2]^2-12 K[1]^3} a-3 \sqrt {81 a^2 K[2]^2-12 K[1]^3}\right ) K[1]+243\ 2^{2/3} \sqrt [3]{3} a K[2]^3 \left (\sqrt {27 a^2 K[2]^2-4 K[1]^3}-3 \sqrt {3} a K[2]\right )\right )}{\left (4 (2 a-3) K[1]^3+27 K[2]^2\right )^2 \sqrt {27 a^2 K[2]^2-4 K[1]^3} \left (\sqrt {81 a^2 K[2]^2-12 K[1]^3}-9 a K[2]\right )^{2/3}}dK[1]+9 \sqrt [3]{2} \sqrt [6]{3} K[2] \left (3 \sqrt {3} a K[2]+\sqrt {27 a^2 K[2]^2-4 x^3}\right ) \left (\sqrt {81 a^2 K[2]^2-12 x^3}-9 a K[2]\right )^{2/3}}{9 \left (4 (2 a-3) K[2] x^4+27 K[2]^3 x\right )}dK[2],y(x)\right ],\text {Solve}\left [c_1=\int _1^x\frac {96 (a-1) K[3]^4+4 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) \left (\sqrt {81 a^2 y(x)^2-12 K[3]^3}-9 a y(x)\right )^{2/3} K[3]^3-2\ 2^{2/3} \sqrt [3]{3} \left (3 i+\sqrt {3}\right ) \sqrt {27 a^2 y(x)^2-4 K[3]^3} \sqrt [3]{\sqrt {81 a^2 y(x)^2-12 K[3]^3}-9 a y(x)} K[3]^2+9 y(x) \left (i \sqrt [3]{2} \sqrt [6]{3} \left (i+\sqrt {3}\right ) \sqrt {27 a^2 y(x)^2-4 K[3]^3} \left (\sqrt {81 a^2 y(x)^2-12 K[3]^3}-9 a y(x)\right )^{2/3}-2 i 2^{2/3} \sqrt [3]{3} \left (-i+\sqrt {3}\right ) (a-1) K[3]^2 \sqrt [3]{\sqrt {81 a^2 y(x)^2-12 K[3]^3}-9 a y(x)}\right )-27 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) a y(x)^2 \left (\sqrt {81 a^2 y(x)^2-12 K[3]^3}-9 a y(x)\right )^{2/3}}{48 (2 a-3) K[3]^5+324 y(x)^2 K[3]^2}dK[3]+\int _1^{y(x)}\frac {-48 x^4-4 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) \left (\sqrt {81 a^2 K[4]^2-12 x^3}-9 a K[4]\right )^{2/3} x^3+2\ 2^{2/3} \sqrt [3]{3} \left (9 \left (1+i \sqrt {3}\right ) (a-1) K[4]+\left (3 i+\sqrt {3}\right ) \sqrt {27 a^2 K[4]^2-4 x^3}\right ) \sqrt [3]{\sqrt {81 a^2 K[4]^2-12 x^3}-9 a K[4]} x^2+324 K[4]^2 x-18 \left (4 (2 a-3) K[4] x^4+27 K[4]^3 x\right ) \int _1^x\frac {8\ 2^{2/3} \sqrt [3]{3} \left (3 i+\sqrt {3}\right ) (3-2 a)^2 K[3]^6-4 \sqrt [3]{2} \sqrt [6]{3} \left (\left (-3 i+\sqrt {3}\right ) \sqrt {27 a^2 K[4]^2-4 K[3]^3} (3-2 a)^2+9 i \left (i+\sqrt {3}\right ) \left (4 a^3-4 a^2-3 a+6\right ) K[4]\right ) \sqrt [3]{\sqrt {81 a^2 K[4]^2-12 K[3]^3}-9 a K[4]} K[3]^4+18\ 2^{2/3} \sqrt [3]{3} K[4] \left (3 \left (3 i+\sqrt {3}\right ) \left (8 a^3-12 a^2+2 a+3\right ) K[4]-2 i \left (-i+\sqrt {3}\right ) \left (4 a^2-6 a+3\right ) \sqrt {27 a^2 K[4]^2-4 K[3]^3}\right ) K[3]^3-432 (a-1) K[4] \sqrt {27 a^2 K[4]^2-4 K[3]^3} \left (\sqrt {81 a^2 K[4]^2-12 K[3]^3}-9 a K[4]\right )^{2/3} K[3]^2+27 \sqrt [3]{2} \sqrt [6]{3} K[4]^2 \left (36 i \left (i+\sqrt {3}\right ) K[4] a^2+\left (9-9 i \sqrt {3}\right ) K[4] a+4 \left (-3 i+\sqrt {3}\right ) \sqrt {27 a^2 K[4]^2-4 K[3]^3} a-3 \left (-3 i+\sqrt {3}\right ) \sqrt {27 a^2 K[4]^2-4 K[3]^3}\right ) \sqrt [3]{\sqrt {81 a^2 K[4]^2-12 K[3]^3}-9 a K[4]} K[3]+243\ 2^{2/3} \sqrt [3]{3} a K[4]^3 \left (\left (1+i \sqrt {3}\right ) \sqrt {27 a^2 K[4]^2-4 K[3]^3}-3 \left (3 i+\sqrt {3}\right ) a K[4]\right )}{\left (4 (2 a-3) K[3]^3+27 K[4]^2\right )^2 \sqrt {27 a^2 K[4]^2-4 K[3]^3} \left (\sqrt {81 a^2 K[4]^2-12 K[3]^3}-9 a K[4]\right )^{2/3}}dK[3]+9 \sqrt [3]{2} \sqrt [6]{3} K[4] \left (3 \left (-3 i+\sqrt {3}\right ) a K[4]+\left (1-i \sqrt {3}\right ) \sqrt {27 a^2 K[4]^2-4 x^3}\right ) \left (\sqrt {81 a^2 K[4]^2-12 x^3}-9 a K[4]\right )^{2/3}}{72 (2 a-3) K[4] x^4+486 K[4]^3 x}dK[4],y(x)\right ],\text {Solve}\left [c_1=\int _1^x\frac {2 \left (48 (a-1) K[5]^2+2 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) \left (\sqrt {81 a^2 y(x)^2-12 K[5]^3}-9 a y(x)\right )^{2/3} K[5]-2^{2/3} \sqrt [3]{3} \left (-3 i+\sqrt {3}\right ) \sqrt {27 a^2 y(x)^2-4 K[5]^3} \sqrt [3]{\sqrt {81 a^2 y(x)^2-12 K[5]^3}-9 a y(x)}\right ) K[5]^2+9 y(x) \left (2 i 2^{2/3} \sqrt [3]{3} \left (i+\sqrt {3}\right ) (a-1) \sqrt [3]{\sqrt {81 a^2 y(x)^2-12 K[5]^3}-9 a y(x)} K[5]^2+\sqrt [3]{2} \sqrt [6]{3} \left (-1-i \sqrt {3}\right ) \sqrt {27 a^2 y(x)^2-4 K[5]^3} \left (\sqrt {81 a^2 y(x)^2-12 K[5]^3}-9 a y(x)\right )^{2/3}\right )-27 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) a y(x)^2 \left (\sqrt {81 a^2 y(x)^2-12 K[5]^3}-9 a y(x)\right )^{2/3}}{48 (2 a-3) K[5]^5+324 y(x)^2 K[5]^2}dK[5]+\int _1^{y(x)}\frac {-48 x^4-4 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) \left (\sqrt {81 a^2 K[6]^2-12 x^3}-9 a K[6]\right )^{2/3} x^3+2\ 2^{2/3} \sqrt [3]{3} \left (9 \left (1-i \sqrt {3}\right ) (a-1) K[6]+\left (-3 i+\sqrt {3}\right ) \sqrt {27 a^2 K[6]^2-4 x^3}\right ) \sqrt [3]{\sqrt {81 a^2 K[6]^2-12 x^3}-9 a K[6]} x^2+324 K[6]^2 x-18 \left (4 (2 a-3) K[6] x^4+27 K[6]^3 x\right ) \int _1^x\frac {8\ 2^{2/3} \sqrt [3]{3} \left (-3 i+\sqrt {3}\right ) (3-2 a)^2 K[5]^6-4 \sqrt [3]{2} \sqrt [6]{3} \left (\left (3 i+\sqrt {3}\right ) (3-2 a)^2 \sqrt {27 a^2 K[6]^2-4 K[5]^3}-9 i \left (-i+\sqrt {3}\right ) \left (4 a^3-4 a^2-3 a+6\right ) K[6]\right ) \sqrt [3]{\sqrt {81 a^2 K[6]^2-12 K[5]^3}-9 a K[6]} K[5]^4+18\ 2^{2/3} \sqrt [3]{3} K[6] \left (2 i \left (i+\sqrt {3}\right ) \sqrt {27 a^2 K[6]^2-4 K[5]^3} \left (4 a^2-6 a+3\right )+3 \left (-3 i+\sqrt {3}\right ) \left (8 a^3-12 a^2+2 a+3\right ) K[6]\right ) K[5]^3-432 (a-1) K[6] \sqrt {27 a^2 K[6]^2-4 K[5]^3} \left (\sqrt {81 a^2 K[6]^2-12 K[5]^3}-9 a K[6]\right )^{2/3} K[5]^2+27 \sqrt [3]{2} \sqrt [6]{3} K[6]^2 \left (-36 i \left (-i+\sqrt {3}\right ) K[6] a^2+\left (9+9 i \sqrt {3}\right ) K[6] a+4 \left (3 i+\sqrt {3}\right ) \sqrt {27 a^2 K[6]^2-4 K[5]^3} a-3 \left (3 i+\sqrt {3}\right ) \sqrt {27 a^2 K[6]^2-4 K[5]^3}\right ) \sqrt [3]{\sqrt {81 a^2 K[6]^2-12 K[5]^3}-9 a K[6]} K[5]+243\ 2^{2/3} \sqrt [3]{3} a K[6]^3 \left (\left (1-i \sqrt {3}\right ) \sqrt {27 a^2 K[6]^2-4 K[5]^3}-3 \left (-3 i+\sqrt {3}\right ) a K[6]\right )}{\left (4 (2 a-3) K[5]^3+27 K[6]^2\right )^2 \sqrt {27 a^2 K[6]^2-4 K[5]^3} \left (\sqrt {81 a^2 K[6]^2-12 K[5]^3}-9 a K[6]\right )^{2/3}}dK[5]+9 \sqrt [3]{2} \sqrt [6]{3} K[6] \left (3 \left (3 i+\sqrt {3}\right ) a K[6]+\left (1+i \sqrt {3}\right ) \sqrt {27 a^2 K[6]^2-4 x^3}\right ) \left (\sqrt {81 a^2 K[6]^2-12 x^3}-9 a K[6]\right )^{2/3}}{72 (2 a-3) K[6] x^4+486 K[6]^3 x}dK[6],y(x)\right ]\right \}\]
Maple ✓
cpu = 1.636 (sec), leaf count = 1223
\[\left [\frac {\textit {\_C1} \left (48 \left (\frac {i \sqrt {3}\, \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 i \sqrt {3}\, x -\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 x}{12 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}} \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} a -72 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (\frac {i \sqrt {3}\, \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 i \sqrt {3}\, x -\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 x}{12 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}}\right )}{\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}}+x -\frac {i \sqrt {3}\, \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {4}{3}}-144 i \sqrt {3}\, x^{2}+\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {4}{3}}-48 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} x +144 x^{2}}{24 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (2 a -3\right )} = 0, \frac {\textit {\_C1} \left (-48 \left (-\frac {i \sqrt {3}\, \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 i \sqrt {3}\, x +\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}+12 x}{12 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}} \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} a +72 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (-\frac {i \sqrt {3}\, \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 i \sqrt {3}\, x +\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}+12 x}{12 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}}\right )}{\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}}+x +\frac {i \sqrt {3}\, \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {4}{3}}-144 i \sqrt {3}\, x^{2}-\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {4}{3}}+48 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} x -144 x^{2}}{24 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (2 a -3\right )} = 0, \frac {\textit {\_C1} \left (-24 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (\frac {\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}+12 x}{6 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}} a +36 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (\frac {\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}+12 x}{6 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}}\right )}{\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}}}+x +\frac {\left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {4}{3}}+24 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} x +144 x^{2}}{12 \left (-108 a y \left (x \right )+12 \sqrt {81 a^{2} y \left (x \right )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (2 a -3\right )} = 0\right ]\] Mathematica raw input
DSolve[a*y[x] - 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)*a*y[x]^2*(-9*a*y[x] + Sqrt[-12*K[1]^3 + 81*a^2*y[x]^2])^(2/3) + 2*K[1]^2*(24*(-1 + a)*K[1]^2 + 2^(2/3)*3^(5/6)*Sqrt[-4*K[1]^3 + 27*a^2*y[x]^2]*(-9*a*y[x] + Sqrt[-12*K[1]^3 + 81*a^2*y[x]^2])^(1/3) - 2*2^(1/3)*3^(2/3)*K[1]*(-9*a*y[x] + Sqrt[-12*K[1]^3 + 81*a^2*y[x]^2])^(2/3)) + 9*y[x]*(2*2^(2/3)*3^(1/3)*(-1 + a)*K[1]^2*(-9*a*y[x] + Sqrt[-12*K[1]^3 + 81*a^2*y[x]^2])^(1/3) + 2^(1/3)*3^(1/6)*Sqrt[-4*K[1]^3 + 27*a^2*y[x]^2]*(-9*a*y[x] + Sqrt[-12*K[1]^3 + 81*a^2*y[x]^2])^(2/3)))/(6*K[1]^2*(4*(-3 + 2*a)*K[1]^3 + 27*y[x]^2)), {K[1], 1, x}] + Inactive[Integrate][-1/9*(24*x^4 - 162*x*K[2]^2 + 2*2^(2/3)*3^(1/3)*x^2*(9*(-1 + a)*K[2] + Sqrt[-12*x^3 + 81*a^2*K[2]^2])*(-9*a*K[2] + Sqrt[-12*x^3 + 81*a^2*K[2]^2])^(1/3) - 4*2^(1/3)*3^(2/3)*x^3*(-9*a*K[2] + Sqrt[-12*x^3 + 81*a^2*K[2]^2])^(2/3) + 9*2^(1/3)*3^(1/6)*K[2]*(3*Sqrt[3]*a*K[2] + Sqrt[-4*x^3 + 27*a^2*K[2]^2])*(-9*a*K[2] + Sqrt[-12*x^3 + 81*a^2*K[2]^2])^(2/3) + 9*(4*(-3 + 2*a)*x^4*K[2] + 27*x*K[2]^3)*Inactive[Integrate][(-2*(8*2^(2/3)*3^(5/6)*(3 - 2*a)^2*K[1]^6 + 243*2^(2/3)*3^(1/3)*a*K[2]^3*(-3*Sqrt[3]*a*K[2] + Sqrt[-4*K[1]^3 + 27*a^2*K[2]^2]) + 18*2^(2/3)*3^(1/3)*K[1]^3*K[2]*(3*Sqrt[3]*(3 + 2*a - 12*a^2 + 8*a^3)*K[2] - 2*(3 - 6*a + 4*a^2)*Sqrt[-4*K[1]^3 + 27*a^2*K[2]^2]) + 216*(-1 + a)*K[1]^2*K[2]*Sqrt[-4*K[1]^3 + 27*a^2*K[2]^2]*(-9*a*K[2] + Sqrt[-12*K[1]^3 + 81*a^2*K[2]^2])^(2/3) - 4*2^(1/3)*3^(1/6)*K[1]^4*(-9*a*K[2] + Sqrt[-12*K[1]^3 + 81*a^2*K[2]^2])^(1/3)*(-9*(6 - 3*a - 4*a^2 + 4*a^3)*K[2] + (3 - 2*a)^2*Sqrt[-12*K[1]^3 + 81*a^2*K[2]^2]) + 27*2^(1/3)*3^(1/6)*K[1]*K[2]^2*(-9*a*K[2] + Sqrt[-12*K[1]^3 + 81*a^2*K[2]^2])^(1/3)*(9*a*K[2] - 36*a^2*K[2] - 3*Sqrt[-12*K[1]^3 + 81*a^2*K[2]^2] + 4*a*Sqrt[-12*K[1]^3 + 81*a^2*K[2]^2])))/((4*(-3 + 2*a)*K[1]^3 + 27*K[2]^2)^2*Sqrt[-4*K[1]^3 + 27*a^2*K[2]^2]*(-9*a*K[2] + Sqrt[-12*K[1]^3 + 81*a^2*K[2]^2])^(2/3)), {K[1], 1, x}])/(4*(-3 + 2*a)*x^4*K[2] + 27*x*K[2]^3), {K[2], 1, y[x]}], y[x]], Solve[C[1] == Inactive[Integrate][(96*(-1 + a)*K[3]^4 - 2*2^(2/3)*3^(1/3)*(3*I + Sqrt[3])*K[3]^2*Sqrt[-4*K[3]^3 + 27*a^2*y[x]^2]*(-9*a*y[x] + Sqrt[-12*K[3]^3 + 81*a^2*y[x]^2])^(1/3) + 4*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*K[3]^3*(-9*a*y[x] + Sqrt[-12*K[3]^3 + 81*a^2*y[x]^2])^(2/3) - 27*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*a*y[x]^2*(-9*a*y[x] + Sqrt[-12*K[3]^3 + 81*a^2*y[x]^2])^(2/3) + 9*y[x]*((-2*I)*2^(2/3)*3^(1/3)*(-I + Sqrt[3])*(-1 + a)*K[3]^2*(-9*a*y[x] + Sqrt[-12*K[3]^3 + 81*a^2*y[x]^2])^(1/3) + I*2^(1/3)*3^(1/6)*(I + Sqrt[3])*Sqrt[-4*K[3]^3 + 27*a^2*y[x]^2]*(-9*a*y[x] + Sqrt[-12*K[3]^3 + 81*a^2*y[x]^2])^(2/3)))/(48*(-3 + 2*a)*K[3]^5 + 324*K[3]^2*y[x]^2), {K[3], 1, x}] + Inactive[Integrate][(-48*x^4 + 324*x*K[4]^2 + 2*2^(2/3)*3^(1/3)*x^2*(9*(1 + I*Sqrt[3])*(-1 + a)*K[4] + (3*I + Sqrt[3])*Sqrt[-4*x^3 + 27*a^2*K[4]^2])*(-9*a*K[4] + Sqrt[-12*x^3 + 81*a^2*K[4]^2])^(1/3) - 4*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*x^3*(-9*a*K[4] + Sqrt[-12*x^3 + 81*a^2*K[4]^2])^(2/3) + 9*2^(1/3)*3^(1/6)*K[4]*(3*(-3*I + Sqrt[3])*a*K[4] + (1 - I*Sqrt[3])*Sqrt[-4*x^3 + 27*a^2*K[4]^2])*(-9*a*K[4] + Sqrt[-12*x^3 + 81*a^2*K[4]^2])^(2/3) - 18*(4*(-3 + 2*a)*x^4*K[4] + 27*x*K[4]^3)*Inactive[Integrate][(8*2^(2/3)*3^(1/3)*(3*I + Sqrt[3])*(3 - 2*a)^2*K[3]^6 + 243*2^(2/3)*3^(1/3)*a*K[4]^3*(-3*(3*I + Sqrt[3])*a*K[4] + (1 + I*Sqrt[3])*Sqrt[-4*K[3]^3 + 27*a^2*K[4]^2]) + 18*2^(2/3)*3^(1/3)*K[3]^3*K[4]*(3*(3*I + Sqrt[3])*(3 + 2*a - 12*a^2 + 8*a^3)*K[4] - (2*I)*(-I + Sqrt[3])*(3 - 6*a + 4*a^2)*Sqrt[-4*K[3]^3 + 27*a^2*K[4]^2]) - 4*2^(1/3)*3^(1/6)*K[3]^4*((9*I)*(I + Sqrt[3])*(6 - 3*a - 4*a^2 + 4*a^3)*K[4] + (-3*I + Sqrt[3])*(3 - 2*a)^2*Sqrt[-4*K[3]^3 + 27*a^2*K[4]^2])*(-9*a*K[4] + Sqrt[-12*K[3]^3 + 81*a^2*K[4]^2])^(1/3) + 27*2^(1/3)*3^(1/6)*K[3]*K[4]^2*((9 - (9*I)*Sqrt[3])*a*K[4] + (36*I)*(I + Sqrt[3])*a^2*K[4] - 3*(-3*I + Sqrt[3])*Sqrt[-4*K[3]^3 + 27*a^2*K[4]^2] + 4*(-3*I + Sqrt[3])*a*Sqrt[-4*K[3]^3 + 27*a^2*K[4]^2])*(-9*a*K[4] + Sqrt[-12*K[3]^3 + 81*a^2*K[4]^2])^(1/3) - 432*(-1 + a)*K[3]^2*K[4]*Sqrt[-4*K[3]^3 + 27*a^2*K[4]^2]*(-9*a*K[4] + Sqrt[-12*K[3]^3 + 81*a^2*K[4]^2])^(2/3))/((4*(-3 + 2*a)*K[3]^3 + 27*K[4]^2)^2*Sqrt[-4*K[3]^3 + 27*a^2*K[4]^2]*(-9*a*K[4] + Sqrt[-12*K[3]^3 + 81*a^2*K[4]^2])^(2/3)), {K[3], 1, x}])/(72*(-3 + 2*a)*x^4*K[4] + 486*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])*a*y[x]^2*(-9*a*y[x] + Sqrt[-12*K[5]^3 + 81*a^2*y[x]^2])^(2/3) + 2*K[5]^2*(48*(-1 + a)*K[5]^2 - 2^(2/3)*3^(1/3)*(-3*I + Sqrt[3])*Sqrt[-4*K[5]^3 + 27*a^2*y[x]^2]*(-9*a*y[x] + Sqrt[-12*K[5]^3 + 81*a^2*y[x]^2])^(1/3) + 2*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*K[5]*(-9*a*y[x] + Sqrt[-12*K[5]^3 + 81*a^2*y[x]^2])^(2/3)) + 9*y[x]*((2*I)*2^(2/3)*3^(1/3)*(I + Sqrt[3])*(-1 + a)*K[5]^2*(-9*a*y[x] + Sqrt[-12*K[5]^3 + 81*a^2*y[x]^2])^(1/3) + 2^(1/3)*3^(1/6)*(-1 - I*Sqrt[3])*Sqrt[-4*K[5]^3 + 27*a^2*y[x]^2]*(-9*a*y[x] + Sqrt[-12*K[5]^3 + 81*a^2*y[x]^2])^(2/3)))/(48*(-3 + 2*a)*K[5]^5 + 324*K[5]^2*y[x]^2), {K[5], 1, x}] + Inactive[Integrate][(-48*x^4 + 324*x*K[6]^2 + 2*2^(2/3)*3^(1/3)*x^2*(9*(1 - I*Sqrt[3])*(-1 + a)*K[6] + (-3*I + Sqrt[3])*Sqrt[-4*x^3 + 27*a^2*K[6]^2])*(-9*a*K[6] + Sqrt[-12*x^3 + 81*a^2*K[6]^2])^(1/3) - 4*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*x^3*(-9*a*K[6] + Sqrt[-12*x^3 + 81*a^2*K[6]^2])^(2/3) + 9*2^(1/3)*3^(1/6)*K[6]*(3*(3*I + Sqrt[3])*a*K[6] + (1 + I*Sqrt[3])*Sqrt[-4*x^3 + 27*a^2*K[6]^2])*(-9*a*K[6] + Sqrt[-12*x^3 + 81*a^2*K[6]^2])^(2/3) - 18*(4*(-3 + 2*a)*x^4*K[6] + 27*x*K[6]^3)*Inactive[Integrate][(8*2^(2/3)*3^(1/3)*(-3*I + Sqrt[3])*(3 - 2*a)^2*K[5]^6 + 243*2^(2/3)*3^(1/3)*a*K[6]^3*(-3*(-3*I + Sqrt[3])*a*K[6] + (1 - I*Sqrt[3])*Sqrt[-4*K[5]^3 + 27*a^2*K[6]^2]) + 18*2^(2/3)*3^(1/3)*K[5]^3*K[6]*(3*(-3*I + Sqrt[3])*(3 + 2*a - 12*a^2 + 8*a^3)*K[6] + (2*I)*(I + Sqrt[3])*(3 - 6*a + 4*a^2)*Sqrt[-4*K[5]^3 + 27*a^2*K[6]^2]) - 4*2^(1/3)*3^(1/6)*K[5]^4*((-9*I)*(-I + Sqrt[3])*(6 - 3*a - 4*a^2 + 4*a^3)*K[6] + (3*I + Sqrt[3])*(3 - 2*a)^2*Sqrt[-4*K[5]^3 + 27*a^2*K[6]^2])*(-9*a*K[6] + Sqrt[-12*K[5]^3 + 81*a^2*K[6]^2])^(1/3) + 27*2^(1/3)*3^(1/6)*K[5]*K[6]^2*((9 + (9*I)*Sqrt[3])*a*K[6] - (36*I)*(-I + Sqrt[3])*a^2*K[6] - 3*(3*I + Sqrt[3])*Sqrt[-4*K[5]^3 + 27*a^2*K[6]^2] + 4*(3*I + Sqrt[3])*a*Sqrt[-4*K[5]^3 + 27*a^2*K[6]^2])*(-9*a*K[6] + Sqrt[-12*K[5]^3 + 81*a^2*K[6]^2])^(1/3) - 432*(-1 + a)*K[5]^2*K[6]*Sqrt[-4*K[5]^3 + 27*a^2*K[6]^2]*(-9*a*K[6] + Sqrt[-12*K[5]^3 + 81*a^2*K[6]^2])^(2/3))/((4*(-3 + 2*a)*K[5]^3 + 27*K[6]^2)^2*Sqrt[-4*K[5]^3 + 27*a^2*K[6]^2]*(-9*a*K[6] + Sqrt[-12*K[5]^3 + 81*a^2*K[6]^2])^(2/3)), {K[5], 1, x}])/(72*(-3 + 2*a)*x^4*K[6] + 486*x*K[6]^3), {K[6], 1, y[x]}], y[x]]}
Maple raw input
dsolve(diff(y(x),x)^3-x*diff(y(x),x)+a*y(x) = 0, y(x))
Maple raw output
[_C1*(48*(1/12*(I*3^(1/2)*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)-12*I*3^(1/2)*x-(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)-12*x)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(1/3))^(1/(a-1))*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*a-72*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*(1/12*(I*3^(1/2)*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)-12*I*3^(1/2)*x-(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)-12*x)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(1/3))^(1/(a-1)))/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)+x-1/24*(I*3^(1/2)*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(4/3)-144*I*3^(1/2)*x^2+(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(4/3)-48*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*x+144*x^2)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)/(2*a-3) = 0, _C1*(-48*(-1/12*(I*3^(1/2)*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)-12*I*3^(1/2)*x+(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)+12*x)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(1/3))^(1/(a-1))*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*a+72*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*(-1/12*(I*3^(1/2)*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)-12*I*3^(1/2)*x+(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)+12*x)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(1/3))^(1/(a-1)))/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)+x+1/24*(I*3^(1/2)*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(4/3)-144*I*3^(1/2)*x^2-(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(4/3)+48*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*x-144*x^2)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)/(2*a-3) = 0, _C1*(-24*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*(1/6*((-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)+12*x)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(1/3))^(1/(a-1))*a+36*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*(1/6*((-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)+12*x)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(1/3))^(1/(a-1)))/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)+x+1/12*((-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(4/3)+24*(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)*x+144*x^2)/(-108*a*y(x)+12*(81*a^2*y(x)^2-12*x^3)^(1/2))^(2/3)/(2*a-3) = 0]