\[ y^{(3)}(x) \left (y'(x)^2+1\right )-y''(x)^2 \left (a+3 y'(x)\right )=0 \] ✗ Mathematica : cpu = 299.997 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 1.273 (sec), leaf count = 789
\[ \left \{ y \left ( x \right ) =\int \!{\frac {\sin \left ( {\it RootOf} \left ( {{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}{a}^{4}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,{a}^{4}x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{a}^{4}{x}^{2}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}{a}^{2}+4\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,{a}^{2}x+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{a}^{2}{x}^{2}-2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{\it \_C2}\,{a}^{3}-2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{a}^{3}x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{x}^{2}-2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{\it \_C2}\,a-2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,ax+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}-1 \right ) \right ) }{\cos \left ( {\it RootOf} \left ( {{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}{a}^{4}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,{a}^{4}x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{a}^{4}{x}^{2}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}{a}^{2}+4\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,{a}^{2}x+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{a}^{2}{x}^{2}-2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{\it \_C2}\,{a}^{3}-2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{a}^{3}x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{x}^{2}-2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{\it \_C2}\,a-2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,ax+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}-1 \right ) \right ) }}\,{\rm d}x+{\it \_C3},y \left ( x \right ) =\int \!{\frac {\sin \left ( {\it RootOf} \left ( {{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}{a}^{4}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,{a}^{4}x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{a}^{4}{x}^{2}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}{a}^{2}+4\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,{a}^{2}x+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{a}^{2}{x}^{2}+2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{\it \_C2}\,{a}^{3}+2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{a}^{3}x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{x}^{2}+2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{\it \_C2}\,a+2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,ax+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}-1 \right ) \right ) }{\cos \left ( {\it RootOf} \left ( {{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}{a}^{4}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,{a}^{4}x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{a}^{4}{x}^{2}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}{a}^{2}+4\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,{a}^{2}x+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{a}^{2}{x}^{2}+2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{\it \_C2}\,{a}^{3}+2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{a}^{3}x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{{\it \_C2}}^{2}+2\,{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{\it \_C2}\,x+{{\rm e}^{2\,a{\it \_Z}}}{{\it \_C1}}^{2}{x}^{2}+2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,{\it \_C2}\,a+2\,{{\rm e}^{a{\it \_Z}}}\cos \left ( {\it \_Z} \right ) {\it \_C1}\,ax+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}-1 \right ) \right ) }}\,{\rm d}x+{\it \_C3} \right \} \]