\[ y''(x)^2 \left (-a-3 y'(x)\right )+y^{(3)}(x) \left (y'(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.492681 (sec), leaf count = 187
\[\left \{\left \{y(x)\to c_3-\frac {\left (1-i \text {InverseFunction}\left [\frac {(\text {$\#$1}-a) e^{-a \tan ^{-1}(\text {$\#$1})}}{\sqrt {\text {$\#$1}^2+1} \left (a^2+1\right ) c_1}\& \right ][x+c_2]\right ){}^{-\frac {1}{2}-\frac {i a}{2}} \left (1+i \text {InverseFunction}\left [\frac {(\text {$\#$1}-a) e^{-a \tan ^{-1}(\text {$\#$1})}}{\sqrt {\text {$\#$1}^2+1} \left (a^2+1\right ) c_1}\& \right ][x+c_2]\right ){}^{\frac {1}{2} i (a+i)} \left (1+a \text {InverseFunction}\left [\frac {(\text {$\#$1}-a) e^{-a \tan ^{-1}(\text {$\#$1})}}{\sqrt {\text {$\#$1}^2+1} \left (a^2+1\right ) c_1}\& \right ][x+c_2]\right )}{\left (a^2+1\right ) c_1}\right \}\right \}\] ✓ Maple : cpu = 1.487 (sec), leaf count = 789
\[\left \{y \left (x \right ) = c_{3}+\int \frac {\sin \left (\RootOf \left (c_{1}^{2} c_{2}^{2} a^{4} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} c_{1}^{2} a^{4} x \,{\mathrm e}^{2 \textit {\_Z} a}+c_{1}^{2} a^{4} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{1}^{2} c_{2}^{2} a^{2} {\mathrm e}^{2 \textit {\_Z} a}+4 c_{2} c_{1}^{2} a^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+2 c_{1}^{2} a^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}-2 c_{1} c_{2} a^{3} \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}-2 c_{1} a^{3} x \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+c_{1}^{2} c_{2}^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} c_{1}^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+c_{1}^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}-2 c_{1} c_{2} a \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}-2 c_{1} a x \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+a^{2} \left (\cos ^{2}\left (\textit {\_Z} \right )\right )+\cos ^{2}\left (\textit {\_Z} \right )-1\right )\right )}{\cos \left (\RootOf \left (c_{1}^{2} c_{2}^{2} a^{4} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} c_{1}^{2} a^{4} x \,{\mathrm e}^{2 \textit {\_Z} a}+c_{1}^{2} a^{4} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{1}^{2} c_{2}^{2} a^{2} {\mathrm e}^{2 \textit {\_Z} a}+4 c_{2} c_{1}^{2} a^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+2 c_{1}^{2} a^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}-2 c_{1} c_{2} a^{3} \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}-2 c_{1} a^{3} x \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+c_{1}^{2} c_{2}^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} c_{1}^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+c_{1}^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}-2 c_{1} c_{2} a \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}-2 c_{1} a x \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+a^{2} \left (\cos ^{2}\left (\textit {\_Z} \right )\right )+\cos ^{2}\left (\textit {\_Z} \right )-1\right )\right )}d x, y \left (x \right ) = c_{3}+\int \frac {\sin \left (\RootOf \left (c_{1}^{2} c_{2}^{2} a^{4} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} c_{1}^{2} a^{4} x \,{\mathrm e}^{2 \textit {\_Z} a}+c_{1}^{2} a^{4} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{1}^{2} c_{2}^{2} a^{2} {\mathrm e}^{2 \textit {\_Z} a}+4 c_{2} c_{1}^{2} a^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+2 c_{1}^{2} a^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{1} c_{2} a^{3} \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+2 c_{1} a^{3} x \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+c_{1}^{2} c_{2}^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} c_{1}^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+c_{1}^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{1} c_{2} a \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+2 c_{1} a x \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+a^{2} \left (\cos ^{2}\left (\textit {\_Z} \right )\right )+\cos ^{2}\left (\textit {\_Z} \right )-1\right )\right )}{\cos \left (\RootOf \left (c_{1}^{2} c_{2}^{2} a^{4} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} c_{1}^{2} a^{4} x \,{\mathrm e}^{2 \textit {\_Z} a}+c_{1}^{2} a^{4} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{1}^{2} c_{2}^{2} a^{2} {\mathrm e}^{2 \textit {\_Z} a}+4 c_{2} c_{1}^{2} a^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+2 c_{1}^{2} a^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{1} c_{2} a^{3} \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+2 c_{1} a^{3} x \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+c_{1}^{2} c_{2}^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} c_{1}^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+c_{1}^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{1} c_{2} a \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+2 c_{1} a x \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a}+a^{2} \left (\cos ^{2}\left (\textit {\_Z} \right )\right )+\cos ^{2}\left (\textit {\_Z} \right )-1\right )\right )}d x\right \}\]