ODE
\[ -a x y'(x)+x^3+y'(x)^3=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Use new variable
Mathematica ✓
cpu = 145.76 (sec), leaf count = 349
\[\left \{\left \{y(x)\to \int _1^x\frac {2 \sqrt [3]{3} a K[1]+\sqrt [3]{2} \left (\sqrt {81 K[1]^6-12 a^3 K[1]^3}-9 K[1]^3\right )^{2/3}}{6^{2/3} \sqrt [3]{\sqrt {81 K[1]^6-12 a^3 K[1]^3}-9 K[1]^3}}dK[1]+c_1\right \},\left \{y(x)\to \int _1^x\frac {i \sqrt [3]{3} \left (i+\sqrt {3}\right ) \left (2 \sqrt {81 K[2]^6-12 a^3 K[2]^3}-18 K[2]^3\right )^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (3 i+\sqrt {3}\right ) a K[2]}{12 \sqrt [3]{\sqrt {81 K[2]^6-12 a^3 K[2]^3}-9 K[2]^3}}dK[2]+c_1\right \},\left \{y(x)\to \int _1^x\frac {\sqrt [3]{3} \left (-1-i \sqrt {3}\right ) \left (2 \sqrt {81 K[3]^6-12 a^3 K[3]^3}-18 K[3]^3\right )^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (-3 i+\sqrt {3}\right ) a K[3]}{12 \sqrt [3]{\sqrt {81 K[3]^6-12 a^3 K[3]^3}-9 K[3]^3}}dK[3]+c_1\right \}\right \}\]
Maple ✓
cpu = 0.195 (sec), leaf count = 300
\[\left [y \left (x \right ) = \int \frac {i \left (i \left (-108 x^{3}+12 \sqrt {-3 x^{3} \left (4 a^{3}-27 x^{3}\right )}\right )^{\frac {2}{3}}+12 i a x -\left (-108 x^{3}+12 \sqrt {-3 x^{3} \left (4 a^{3}-27 x^{3}\right )}\right )^{\frac {2}{3}} \sqrt {3}+12 \sqrt {3}\, a x \right )}{12 \left (-108 x^{3}+12 \sqrt {-3 x^{3} \left (4 a^{3}-27 x^{3}\right )}\right )^{\frac {1}{3}}}d x +\textit {\_C1}, y \left (x \right ) = \int \frac {i \left (\left (-108 x^{3}+12 \sqrt {-3 x^{3} \left (4 a^{3}-27 x^{3}\right )}\right )^{\frac {2}{3}} \sqrt {3}-12 \sqrt {3}\, a x +i \left (-108 x^{3}+12 \sqrt {-3 x^{3} \left (4 a^{3}-27 x^{3}\right )}\right )^{\frac {2}{3}}+12 i a x \right )}{12 \left (-108 x^{3}+12 \sqrt {-3 x^{3} \left (4 a^{3}-27 x^{3}\right )}\right )^{\frac {1}{3}}}d x +\textit {\_C1}, y \left (x \right ) = \int \frac {\left (-108 x^{3}+12 \sqrt {-3 x^{3} \left (4 a^{3}-27 x^{3}\right )}\right )^{\frac {2}{3}}+12 a x}{6 \left (-108 x^{3}+12 \sqrt {-3 x^{3} \left (4 a^{3}-27 x^{3}\right )}\right )^{\frac {1}{3}}}d x +\textit {\_C1}\right ]\] Mathematica raw input
DSolve[x^3 - a*x*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1] + Inactive[Integrate][(2*3^(1/3)*a*K[1] + 2^(1/3)*(-9*K[1]^3 + Sqrt[-12*a^3*K[1]^3 + 81*K[1]^6])^(2/3))/(6^(2/3)*(-9*K[1]^3 + Sqrt[-12*a^3*K[1]^3 + 81*K[1]^6])^(1/3)), {K[1], 1, x}]}, {y[x] -> C[1] + Inactive[Integrate][(-2*2^(1/3)*3^(1/6)*(3*I + Sqrt[3])*a*K[2] + I*3^(1/3)*(I + Sqrt[3])*(-18*K[2]^3 + 2*Sqrt[-12*a^3*K[2]^3 + 81*K[2]^6])^(2/3))/(12*(-9*K[2]^3 + Sqrt[-12*a^3*K[2]^3 + 81*K[2]^6])^(1/3)), {K[2], 1, x}]}, {y[x] -> C[1] + Inactive[Integrate][(-2*2^(1/3)*3^(1/6)*(-3*I + Sqrt[3])*a*K[3] + 3^(1/3)*(-1 - I*Sqrt[3])*(-18*K[3]^3 + 2*Sqrt[-12*a^3*K[3]^3 + 81*K[3]^6])^(2/3))/(12*(-9*K[3]^3 + Sqrt[-12*a^3*K[3]^3 + 81*K[3]^6])^(1/3)), {K[3], 1, x}]}}
Maple raw input
dsolve(diff(y(x),x)^3-a*x*diff(y(x),x)+x^3 = 0, y(x))
Maple raw output
[y(x) = Int(1/12*I*(I*(-108*x^3+12*(-3*x^3*(4*a^3-27*x^3))^(1/2))^(2/3)+12*I*a*x-(-108*x^3+12*(-3*x^3*(4*a^3-27*x^3))^(1/2))^(2/3)*3^(1/2)+12*3^(1/2)*a*x)/(-108*x^3+12*(-3*x^3*(4*a^3-27*x^3))^(1/2))^(1/3),x)+_C1, y(x) = Int(1/12*I*((-108*x^3+12*(-3*x^3*(4*a^3-27*x^3))^(1/2))^(2/3)*3^(1/2)-12*3^(1/2)*a*x+I*(-108*x^3+12*(-3*x^3*(4*a^3-27*x^3))^(1/2))^(2/3)+12*I*a*x)/(-108*x^3+12*(-3*x^3*(4*a^3-27*x^3))^(1/2))^(1/3),x)+_C1, y(x) = Int(1/6*((-108*x^3+12*(-3*x^3*(4*a^3-27*x^3))^(1/2))^(2/3)+12*a*x)/(-108*x^3+12*(-3*x^3*(4*a^3-27*x^3))^(1/2))^(1/3),x)+_C1]