\[ 2 y(x) y''(x)+y'(x)^2+1=0 \] ✓ Mathematica : cpu = 0.365993 (sec), leaf count = 166
DSolve[1 + Derivative[1][y][x]^2 + 2*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}} \left (\text {$\#$1}-e^{2 c_1}\right )+e^{3 c_1} \sqrt {1-\text {$\#$1} e^{-2 c_1}} \sin ^{-1}\left (\sqrt {\text {$\#$1}} e^{-c_1}\right )}{\sqrt {-\text {$\#$1}+e^{2 c_1}}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {\text {$\#$1}} \left (\text {$\#$1}-e^{2 c_1}\right )+e^{3 c_1} \sqrt {1-\text {$\#$1} e^{-2 c_1}} \sin ^{-1}\left (\sqrt {\text {$\#$1}} e^{-c_1}\right )}{\sqrt {-\text {$\#$1}+e^{2 c_1}}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.251 (sec), leaf count = 823
dsolve(2*diff(diff(y(x),x),x)*y(x)+diff(y(x),x)^2+1=0,y(x))
\[y \left (x \right ) = \frac {\tan \left (\RootOf \left (\left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1}^{2} \textit {\_Z}^{2}-4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1} c_{2} \textit {\_Z} -4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1} x \textit {\_Z} +4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{2}^{2}+8 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x c_{2}+4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x^{2}+c_{1}^{2} \textit {\_Z}^{2}-4 c_{1} \textit {\_Z} c_{2}-4 c_{1} \textit {\_Z} x -c_{1}^{2}+4 c_{2}^{2}+8 x c_{2}+4 x^{2}\right )\right ) \left (-\RootOf \left (\left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1}^{2} \textit {\_Z}^{2}-4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1} c_{2} \textit {\_Z} -4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1} x \textit {\_Z} +4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{2}^{2}+8 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x c_{2}+4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x^{2}+c_{1}^{2} \textit {\_Z}^{2}-4 c_{1} \textit {\_Z} c_{2}-4 c_{1} \textit {\_Z} x -c_{1}^{2}+4 c_{2}^{2}+8 x c_{2}+4 x^{2}\right ) c_{1}+2 c_{2}+2 x \right )}{2}+\frac {c_{1}}{2}\]