\[ y'(x)^3+y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.0218305 (sec), leaf count = 330
DSolve[-y[x] + Derivative[1][y][x] + Derivative[1][y][x]^3 == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}-6 \sqrt [3]{2}}d\text {$\#$1}\& \right ]\left [-\frac {x}{6}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{-i 2^{2/3} \sqrt {3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}-6 i \sqrt [3]{2} \sqrt {3}-6 \sqrt [3]{2}}d\text {$\#$1}\& \right ]\left [\frac {x}{12}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{i 2^{2/3} \sqrt {3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+6 i \sqrt [3]{2} \sqrt {3}-6 \sqrt [3]{2}}d\text {$\#$1}\& \right ]\left [\frac {x}{12}+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.153 (sec), leaf count = 249
dsolve(diff(y(x),x)^3+diff(y(x),x)-y(x)=0,y(x))
\[x -\left (\int _{}^{y \left (x \right )}\frac {6 \left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}}{\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {2}{3}}-12}d \textit {\_a} \right )-c_{1} = 0\]