\[ -a y(x) y'(x)-a x+y(x) \sqrt {y'(x)^2+1}=0 \] ✓ Mathematica : cpu = 0.399837 (sec), leaf count = 212
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^6 \left (-x^2\right )+3 a^4 x^2-3 a^2 x^2+2 a^2 x e^{a^2 c_1-c_1}-2 x e^{a^2 c_1-c_1}+e^{2 a^2 c_1-2 c_1}+x^2}}{\sqrt {a^6-3 a^4+3 a^2-1}}\right \},\left \{y(x)\to \frac {\sqrt {a^6 \left (-x^2\right )+3 a^4 x^2-3 a^2 x^2+2 a^2 x e^{a^2 c_1-c_1}-2 x e^{a^2 c_1-c_1}+e^{2 a^2 c_1-2 c_1}+x^2}}{\sqrt {a^6-3 a^4+3 a^2-1}}\right \}\right \}\] ✓ Maple : cpu = 0.248 (sec), leaf count = 215
\[\left \{-c_{1} {\mathrm e}^{\int _{}^{\frac {-a^{2} x -\sqrt {a^{2} x^{2}+\left (a^{2}-1\right ) y \left (x \right )^{2}}}{\left (a^{2}-1\right ) y \left (x \right )}}\frac {\left (-\textit {\_a} +\sqrt {\textit {\_a}^{2}+1}\, a \right ) a}{\sqrt {\textit {\_a}^{2}+1}\, \left (\textit {\_a} a -\sqrt {\textit {\_a}^{2}+1}\right ) \left (\textit {\_a}^{2} a -\sqrt {\textit {\_a}^{2}+1}\, \textit {\_a} +a \right )}d \textit {\_a}}+x = 0, -c_{1} {\mathrm e}^{\int _{}^{\frac {-a^{2} x +\sqrt {a^{2} x^{2}+\left (a^{2}-1\right ) y \left (x \right )^{2}}}{\left (a^{2}-1\right ) y \left (x \right )}}\frac {\left (-\textit {\_a} +\sqrt {\textit {\_a}^{2}+1}\, a \right ) a}{\sqrt {\textit {\_a}^{2}+1}\, \left (\textit {\_a} a -\sqrt {\textit {\_a}^{2}+1}\right ) \left (\textit {\_a}^{2} a -\sqrt {\textit {\_a}^{2}+1}\, \textit {\_a} +a \right )}d \textit {\_a}}+x = 0\right \}\]