\[ 2 y(x) y''(x)+y'(x)^2+1=0 \] ✓ Mathematica : cpu = 0.353967 (sec), leaf count = 166
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}} \left (\text {$\#$1}-e^{2 c_1}\right )+e^{3 c_1} \sqrt {1-\text {$\#$1} e^{-2 c_1}} \sin ^{-1}\left (\sqrt {\text {$\#$1}} e^{-c_1}\right )}{\sqrt {e^{2 c_1}-\text {$\#$1}}}\& \right ][c_2+x]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {\text {$\#$1}} \left (\text {$\#$1}-e^{2 c_1}\right )+e^{3 c_1} \sqrt {1-\text {$\#$1} e^{-2 c_1}} \sin ^{-1}\left (\sqrt {\text {$\#$1}} e^{-c_1}\right )}{\sqrt {e^{2 c_1}-\text {$\#$1}}}\& \right ][c_2+x]\right \}\right \}\] ✓ Maple : cpu = 0.322 (sec), leaf count = 823
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -{\it RootOf} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C1}}^{2}{{\it \_Z}}^{2}-4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,{\it \_C2}\,{\it \_Z}-4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,x{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C2}}^{2}+8\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}x{\it \_C2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{x}^{2}+{{\it \_C1}}^{2}{{\it \_Z}}^{2}-4\,{\it \_C1}\,{\it \_Z}\,{\it \_C2}-4\,{\it \_C1}\,{\it \_Z}\,x-{{\it \_C1}}^{2}+4\,{{\it \_C2}}^{2}+8\,{\it \_C2}\,x+4\,{x}^{2} \right ) {\it \_C1}+2\,x+2\,{\it \_C2} \right ) \tan \left ( {\it RootOf} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C1}}^{2}{{\it \_Z}}^{2}-4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,{\it \_C2}\,{\it \_Z}-4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,x{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C2}}^{2}+8\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}x{\it \_C2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{x}^{2}+{{\it \_C1}}^{2}{{\it \_Z}}^{2}-4\,{\it \_C1}\,{\it \_Z}\,{\it \_C2}-4\,{\it \_C1}\,{\it \_Z}\,x-{{\it \_C1}}^{2}+4\,{{\it \_C2}}^{2}+8\,{\it \_C2}\,x+4\,{x}^{2} \right ) \right ) }{2}}+{\frac {{\it \_C1}}{2}},y \left ( x \right ) ={\frac { \left ( {\it RootOf} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C1}}^{2}{{\it \_Z}}^{2}-4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,{\it \_C2}\,{\it \_Z}-4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,x{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C2}}^{2}+8\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}x{\it \_C2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{x}^{2}+{{\it \_C1}}^{2}{{\it \_Z}}^{2}-4\,{\it \_C1}\,{\it \_Z}\,{\it \_C2}-4\,{\it \_C1}\,{\it \_Z}\,x-{{\it \_C1}}^{2}+4\,{{\it \_C2}}^{2}+8\,{\it \_C2}\,x+4\,{x}^{2} \right ) {\it \_C1}-2\,x-2\,{\it \_C2} \right ) \tan \left ( {\it RootOf} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C1}}^{2}{{\it \_Z}}^{2}-4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,{\it \_C2}\,{\it \_Z}-4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,x{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C2}}^{2}+8\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}x{\it \_C2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{x}^{2}+{{\it \_C1}}^{2}{{\it \_Z}}^{2}-4\,{\it \_C1}\,{\it \_Z}\,{\it \_C2}-4\,{\it \_C1}\,{\it \_Z}\,x-{{\it \_C1}}^{2}+4\,{{\it \_C2}}^{2}+8\,{\it \_C2}\,x+4\,{x}^{2} \right ) \right ) }{2}}+{\frac {{\it \_C1}}{2}},y \left ( x \right ) ={\frac { \left ( -{\it RootOf} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C1}}^{2}{{\it \_Z}}^{2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,{\it \_C2}\,{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,x{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C2}}^{2}+8\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}x{\it \_C2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{x}^{2}+{{\it \_C1}}^{2}{{\it \_Z}}^{2}+4\,{\it \_C1}\,{\it \_Z}\,{\it \_C2}+4\,{\it \_C1}\,{\it \_Z}\,x-{{\it \_C1}}^{2}+4\,{{\it \_C2}}^{2}+8\,{\it \_C2}\,x+4\,{x}^{2} \right ) {\it \_C1}-2\,x-2\,{\it \_C2} \right ) \tan \left ( {\it RootOf} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C1}}^{2}{{\it \_Z}}^{2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,{\it \_C2}\,{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,x{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C2}}^{2}+8\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}x{\it \_C2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{x}^{2}+{{\it \_C1}}^{2}{{\it \_Z}}^{2}+4\,{\it \_C1}\,{\it \_Z}\,{\it \_C2}+4\,{\it \_C1}\,{\it \_Z}\,x-{{\it \_C1}}^{2}+4\,{{\it \_C2}}^{2}+8\,{\it \_C2}\,x+4\,{x}^{2} \right ) \right ) }{2}}+{\frac {{\it \_C1}}{2}},y \left ( x \right ) ={\frac { \left ( {\it RootOf} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C1}}^{2}{{\it \_Z}}^{2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,{\it \_C2}\,{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,x{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C2}}^{2}+8\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}x{\it \_C2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{x}^{2}+{{\it \_C1}}^{2}{{\it \_Z}}^{2}+4\,{\it \_C1}\,{\it \_Z}\,{\it \_C2}+4\,{\it \_C1}\,{\it \_Z}\,x-{{\it \_C1}}^{2}+4\,{{\it \_C2}}^{2}+8\,{\it \_C2}\,x+4\,{x}^{2} \right ) {\it \_C1}+2\,x+2\,{\it \_C2} \right ) \tan \left ( {\it RootOf} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C1}}^{2}{{\it \_Z}}^{2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,{\it \_C2}\,{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{\it \_C1}\,x{\it \_Z}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{{\it \_C2}}^{2}+8\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}x{\it \_C2}+4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}{x}^{2}+{{\it \_C1}}^{2}{{\it \_Z}}^{2}+4\,{\it \_C1}\,{\it \_Z}\,{\it \_C2}+4\,{\it \_C1}\,{\it \_Z}\,x-{{\it \_C1}}^{2}+4\,{{\it \_C2}}^{2}+8\,{\it \_C2}\,x+4\,{x}^{2} \right ) \right ) }{2}}+{\frac {{\it \_C1}}{2}} \right \} \]