\[ y'(x)^3+y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.0238652 (sec), leaf count = 1115
DSolve[-y[x] + Derivative[1][y][x] + Derivative[1][y][x]^3 == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}}{0\ 2 \sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}+2^{2/3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}+2\ 0^2 \sqrt [3]{2}-6 \sqrt [3]{2}}d\text {$\#$1}\& \right ]\left [c_1-\frac {x}{6}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}}{-0 4 \sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}+2^{2/3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}-2^{2/3} i \sqrt {3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}+2\ 0^2 \sqrt [3]{2}-6 \sqrt [3]{2}+2\ 0^2 \sqrt [3]{2} i \sqrt {3}-6 \sqrt [3]{2} i \sqrt {3}}d\text {$\#$1}\& \right ]\left [\frac {x}{12}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}}{-0 4 \sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}+2^{2/3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}+2^{2/3} i \sqrt {3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}+2\ 0^2 \sqrt [3]{2}-6 \sqrt [3]{2}-2\ 0^2 \sqrt [3]{2} i \sqrt {3}+6 \sqrt [3]{2} i \sqrt {3}}d\text {$\#$1}\& \right ]\left [\frac {x}{12}+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.193 (sec), leaf count = 249
dsolve(diff(y(x),x)^3+diff(y(x),x)-y(x)=0,y(x))
\[x -\left (\int _{}^{y \left (x \right )}\frac {6 \left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}}{\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {2}{3}}-12}d \textit {\_a} \right )-c_{1} = 0\]