\[ y^{(3)}(x)-a^2 \left (y'(x)^5+2 y'(x)^3+y'(x)\right )=0 \] ✓ Mathematica : cpu = 10.1927 (sec), leaf count = 145
\[\left \{\left \{y(x)\to \int _1^x\text {InverseFunction}\left [-3 \int \frac {1}{\sqrt {3 \left (a^2\right )^2 \text {$\#$1}^6+9 \left (a^2\right )^2 \text {$\#$1}^4+9 \left (a^2\right )^2 \text {$\#$1}^2+9 c_1}}d\text {$\#$1}\& \right ][c_2-K[1]]dK[1]+c_3\right \},\left \{y(x)\to \int _1^x\text {InverseFunction}\left [3 \int \frac {1}{\sqrt {3 \left (a^2\right )^2 \text {$\#$1}^6+9 \left (a^2\right )^2 \text {$\#$1}^4+9 \left (a^2\right )^2 \text {$\#$1}^2+9 c_1}}d\text {$\#$1}\& \right ][c_2-K[2]]dK[2]+c_3\right \}\right \}\] ✓ Maple : cpu = 0.479 (sec), leaf count = 95
\[y \relax (x ) = \int \RootOf \left (3 \left (\int _{}^{\textit {\_Z}}\frac {1}{\sqrt {3 a^{2} \textit {\_f}^{6}+9 \textit {\_f}^{4} a^{2}+9 \textit {\_f}^{2} a^{2}+9 c_{1}}}d \textit {\_f} \right )+x +c_{2}\right )d x +c_{3}\]