\[ y^{(3)}(x) y(x)+y(x)^3 y'(x)-y'(x) y''(x)=0 \] ✓ Mathematica : cpu = 2.0153 (sec), leaf count = 409
DSolve[y[x]^3*Derivative[1][y][x] - Derivative[1][y][x]*Derivative[2][y][x] + y[x]*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {2 i \sqrt {1+\frac {\text {$\#$1}^2}{2 \left (\sqrt {c_2{}^2-c_1}-c_2\right )}} \sqrt {1-\frac {\text {$\#$1}^2}{2 \left (c_2+\sqrt {c_2{}^2-c_1}\right )}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {1}{\sqrt {c_2{}^2-c_1}-c_2}} \text {$\#$1}}{\sqrt {2}}\right )|\frac {c_2-\sqrt {c_2{}^2-c_1}}{c_2+\sqrt {c_2{}^2-c_1}}\right )}{\sqrt {\frac {1}{\sqrt {c_2{}^2-c_1}-c_2}} \sqrt {-\frac {\text {$\#$1}^4}{2}+2 \text {$\#$1}^2 c_2-2 c_1}}\& \right ][x+c_3]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {2 i \sqrt {1+\frac {\text {$\#$1}^2}{2 \left (\sqrt {c_2{}^2-c_1}-c_2\right )}} \sqrt {1-\frac {\text {$\#$1}^2}{2 \left (c_2+\sqrt {c_2{}^2-c_1}\right )}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {1}{\sqrt {c_2{}^2-c_1}-c_2}} \text {$\#$1}}{\sqrt {2}}\right )|\frac {c_2-\sqrt {c_2{}^2-c_1}}{c_2+\sqrt {c_2{}^2-c_1}}\right )}{\sqrt {\frac {1}{\sqrt {c_2{}^2-c_1}-c_2}} \sqrt {-\frac {\text {$\#$1}^4}{2}+2 \text {$\#$1}^2 c_2-2 c_1}}\& \right ][x+c_3]\right \}\right \}\] ✓ Maple : cpu = 0.439 (sec), leaf count = 77
dsolve(y(x)*diff(diff(diff(y(x),x),x),x)-diff(y(x),x)*diff(diff(y(x),x),x)+y(x)^3*diff(y(x),x)=0,y(x))
\[\int _{}^{y \left (x \right )}-\frac {2}{\sqrt {-\textit {\_a}^{4}+4 \textit {\_a}^{2} c_{2}-4 c_{2}^{2}+4 c_{1}}}d \textit {\_a} -x -c_{3} = 0\]