\[ y'(x)-\sqrt {\frac {y(x)^3+1}{x^3+1}}=0 \] ✓ Mathematica : cpu = 1.6787 (sec), leaf count = 312
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {i (\text {$\#$1}+1) \sqrt {1+\frac {6 i}{\left (\sqrt {3}-3 i\right ) (\text {$\#$1}+1)}} \sqrt {\frac {2}{3}-\frac {4 i}{\left (\sqrt {3}+3 i\right ) (\text {$\#$1}+1)}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {-\frac {6 i}{3 i+\sqrt {3}}}}{\sqrt {\text {$\#$1}+1}}\right )|\frac {3 i+\sqrt {3}}{3 i-\sqrt {3}}\right )}{\sqrt {-\frac {i}{\sqrt {3}+3 i}} \sqrt {\text {$\#$1}^2-\text {$\#$1}+1}}\& \right ]\left [c_1+\frac {i (x+1) \sqrt {1+\frac {6 i}{\left (\sqrt {3}-3 i\right ) (x+1)}} \sqrt {\frac {2}{3}-\frac {4 i}{\left (\sqrt {3}+3 i\right ) (x+1)}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {-\frac {6 i}{3 i+\sqrt {3}}}}{\sqrt {x+1}}\right )|\frac {3 i+\sqrt {3}}{3 i-\sqrt {3}}\right )}{\sqrt {-\frac {i}{\sqrt {3}+3 i}} \sqrt {x^2-x+1}}\right ]\right \}\right \}\]
✓ Maple : cpu = 0.054 (sec), leaf count = 47
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {{{\it \_a}}^{3}+1}}}{d{\it \_a}}+\int ^{x}\!-{1\sqrt {{\frac { \left ( y \left ( x \right ) \right ) ^{3}+1}{{{\it \_a}}^{3}+1}}}{\frac {1}{\sqrt { \left ( y \left ( x \right ) \right ) ^{3}+1}}}}{d{\it \_a}}+{\it \_C1}=0 \right \} \]