ODE
\[ y'(x)^3+y'(x)-y(x)=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 223.943 (sec), leaf count = 3323
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\left (243 \text {$\#$1}^2-27 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+54\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{4/3}}{864 \sqrt [3]{3} \left (-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-2\right )}+\frac {\sqrt {9 \text {$\#$1}^2+\frac {4}{3}} \left (2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )+3 \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )}{36 \sqrt [3]{2} \left (-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-4\right )}-\frac {\left (9 \sqrt {3} \text {$\#$1}+\sqrt {27 \text {$\#$1}^2+4}\right ) \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}}{32\ 3^{5/6}}-\frac {\log (\text {$\#$1})}{3\ 6^{2/3}}\& \right ]\left [c_1-\frac {x}{6^{2/3}}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {i \left (-\frac {\sqrt [3]{3} \left (-i+\sqrt {3}\right ) \left (243 \text {$\#$1}^2-27 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+54\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{4/3}}{-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-2}+\frac {4\ 6^{2/3} \left (3+i \sqrt {3}\right ) \sqrt {27 \text {$\#$1}^2+4} \left (2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )+3 \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )}{-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-4}+9 \sqrt [3]{3} \left (3-i \sqrt {3}\right ) \left (9 \sqrt {3} \text {$\#$1}+\sqrt {27 \text {$\#$1}^2+4}\right ) \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+288 i \sqrt [3]{2} \log (\text {$\#$1})\right )}{3456\ 3^{5/6}}\& \right ]\left [\frac {x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {i \left (-\frac {\sqrt [3]{3} \left (i+\sqrt {3}\right ) \left (243 \text {$\#$1}^2-27 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+54\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{4/3}}{-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-2}+\frac {4\ 6^{2/3} \left (3-i \sqrt {3}\right ) \sqrt {27 \text {$\#$1}^2+4} \left (2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )+3 \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )}{-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-4}+9 \sqrt [3]{3} \left (3+i \sqrt {3}\right ) \left (9 \sqrt {3} \text {$\#$1}+\sqrt {27 \text {$\#$1}^2+4}\right ) \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}-288 i \sqrt [3]{2} \log (\text {$\#$1})\right )}{3456\ 3^{5/6}}\& \right ]\left [\frac {x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ]\right \}\right \}\]
Maple ✓
cpu = 0.689 (sec), leaf count = 245
\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}}{ \left ( 108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12} \right ) ^{2/3}-12}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-12\,{\frac {\sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}}{ \left ( i\sqrt {3}-1 \right ) \left ( -\sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}+\sqrt {3}+3\,i \right ) \left ( \sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}+\sqrt {3}+3\,i \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-12\,{\frac {\sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}}{ \left ( i\sqrt {3}+1 \right ) \left ( \sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}+\sqrt {3}-3\,i \right ) \left ( \sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}-\sqrt {3}+3\,i \right ) }}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[-y[x] + y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[-Log[#1]/(3*6^(2/3)) - ((9*Sqrt[3]*#1 + Sqrt[4 + 27*#1^2])*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3))/(32*3^(5/6)) + (Sqrt[4/3 + 9*#1^2]*(-9*#1 + Sqrt[12 + 81*#1^2])*(2*2^(2/3)*3^(5/6)*ArcTan[1/Sqrt[3] - (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(5/6)*ArcTan[1/Sqrt[3] + (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(1/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(1/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] - 2^(2/3)*3^(1/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)] - 2^(2/3)*3^(1/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)] + 3*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)))/(36*2^(1/3)*(-4 - 27*#1^2 + 3*#1*Sqrt[12 + 81*#1^2])) + ((-9*#1 + Sqrt[12 + 81*#1^2])^(4/3)*(54 + 243*#1^2 - 27*#1*Sqrt[12 + 81*#1^2] - 24*2^(1/3)*3^(1/6)*ArcTan[1/Sqrt[3] - (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 24*2^(1/3)*3^(1/6)*ArcTan[1/Sqrt[3] + (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) + 8*2^(1/3)*3^(2/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) + 8*2^(1/3)*3^(2/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 4*2^(1/3)*3^(2/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 4*2^(1/3)*3^(2/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)))/(864*3^(1/3)*(-2 - 27*#1^2 + 3*#1*Sqrt[12 + 81*#1^2])) & ][-(x/6^(2/3)) + C[1]]}, {y[x] -> InverseFunction[((-I/3456)*((288*I)*2^(1/3)*Log[#1] + 9*3^(1/3)*(3 - I*Sqrt[3])*(9*Sqrt[3]*#1 + Sqrt[4 + 27*#1^2])*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + (4*6^(2/3)*(3 + I*Sqrt[3])*Sqrt[4 + 27*#1^2]*(-9*#1 + Sqrt[12 + 81*#1^2])*(2*2^(2/3)*3^(5/6)*ArcTan[1/Sqrt[3] - (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(5/6)*ArcTan[1/Sqrt[3] + (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(1/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(1/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] - 2^(2/3)*3^(1/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)] - 2^(2/3)*3^(1/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)] + 3*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)))/(-4 - 27*#1^2 + 3*#1*Sqrt[12 + 81*#1^2]) - (3^(1/3)*(-I + Sqrt[3])*(-9*#1 + Sqrt[12 + 81*#1^2])^(4/3)*(54 + 243*#1^2 - 27*#1*Sqrt[12 + 81*#1^2] - 24*2^(1/3)*3^(1/6)*ArcTan[1/Sqrt[3] - (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 24*2^(1/3)*3^(1/6)*ArcTan[1/Sqrt[3] + (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) + 8*2^(1/3)*3^(2/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) + 8*2^(1/3)*3^(2/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 4*2^(1/3)*3^(2/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 4*2^(1/3)*3^(2/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)))/(-2 - 27*#1^2 + 3*#1*Sqrt[12 + 81*#1^2])))/3^(5/6) & ][x/(2*2^(2/3)*3^(5/6)) + C[1]]}, {y[x] -> InverseFunction[((I/3456)*((-288*I)*2^(1/3)*Log[#1] + 9*3^(1/3)*(3 + I*Sqrt[3])*(9*Sqrt[3]*#1 + Sqrt[4 + 27*#1^2])*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + (4*6^(2/3)*(3 - I*Sqrt[3])*Sqrt[4 + 27*#1^2]*(-9*#1 + Sqrt[12 + 81*#1^2])*(2*2^(2/3)*3^(5/6)*ArcTan[1/Sqrt[3] - (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(5/6)*ArcTan[1/Sqrt[3] + (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(1/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] + 2*2^(2/3)*3^(1/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)] - 2^(2/3)*3^(1/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)] - 2^(2/3)*3^(1/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)] + 3*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)))/(-4 - 27*#1^2 + 3*#1*Sqrt[12 + 81*#1^2]) - (3^(1/3)*(I + Sqrt[3])*(-9*#1 + Sqrt[12 + 81*#1^2])^(4/3)*(54 + 243*#1^2 - 27*#1*Sqrt[12 + 81*#1^2] - 24*2^(1/3)*3^(1/6)*ArcTan[1/Sqrt[3] - (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 24*2^(1/3)*3^(1/6)*ArcTan[1/Sqrt[3] + (2/3)^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) + 8*2^(1/3)*3^(2/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) + 8*2^(1/3)*3^(2/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 4*2^(1/3)*3^(2/3)*Log[6 - 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3) - 4*2^(1/3)*3^(2/3)*Log[6 + 2^(2/3)*3^(5/6)*(-9*#1 + Sqrt[12 + 81*#1^2])^(1/3) + 2^(1/3)*3^(2/3)*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)]*(-9*#1 + Sqrt[12 + 81*#1^2])^(2/3)))/(-2 - 27*#1^2 + 3*#1*Sqrt[12 + 81*#1^2])))/3^(5/6) & ][x/(2*2^(2/3)*3^(5/6)) + C[1]]}}
Maple raw input
dsolve(diff(y(x),x)^3+diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
x-Intat(6/((108*_a+12*(81*_a^2+12)^(1/2))^(2/3)-12)*(108*_a+12*(81*_a^2+12)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(-12/(I*3^(1/2)+1)/((108*_a+12*(81*_a^2+12)^(1/2))^(1/3)+3^(1/2)-3*I)/((108*_a+12*(81*_a^2+12)^(1/2))^(1/3)-3^(1/2)+3*I)*(108*_a+12*(81*_a^2+12)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(-12*(108*_a+12*(81*_a^2+12)^(1/2))^(1/3)/(I*3^(1/2)-1)/(-(108*_a+12*(81*_a^2+12)^(1/2))^(1/3)+3^(1/2)+3*I)/((108*_a+12*(81*_a^2+12)^(1/2))^(1/3)+3^(1/2)+3*I),_a = y(x))-_C1 = 0