\[ -a y(x) y'(x)-a x+y(x) \sqrt {y'(x)^2+1}=0 \] ✓ Mathematica : cpu = 0.334332 (sec), leaf count = 126
\[\left \{\left \{y(x)\to -\frac {\sqrt {2 \left (a^2-1\right ) x e^{\left (a^2-1\right ) c_1}+e^{2 \left (a^2-1\right ) c_1}+\left (a^2-1\right )^3 \left (-x^2\right )}}{\sqrt {\left (a^2-1\right )^3}}\right \},\left \{y(x)\to \frac {\sqrt {2 \left (a^2-1\right ) x e^{\left (a^2-1\right ) c_1}+e^{2 \left (a^2-1\right ) c_1}+\left (a^2-1\right )^3 \left (-x^2\right )}}{\sqrt {\left (a^2-1\right )^3}}\right \}\right \}\]
✓ Maple : cpu = 1.421 (sec), leaf count = 215
\[ \left \{ -{{\rm e}^{\int ^{{\frac {1}{ \left ( {a}^{2}-1 \right ) y \left ( x \right ) } \left ( -{a}^{2}x-\sqrt { \left ( {a}^{2}-1 \right ) \left ( y \left ( x \right ) \right ) ^{2}+{a}^{2}{x}^{2}} \right ) }}\!{a \left ( a\sqrt {{{\it \_a}}^{2}+1}-{\it \_a} \right ) {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \left ( {\it \_a}\,a-\sqrt {{{\it \_a}}^{2}+1} \right ) ^{-1} \left ( {{\it \_a}}^{2}a-\sqrt {{{\it \_a}}^{2}+1}{\it \_a}+a \right ) ^{-1}}{d{\it \_a}}}}{\it \_C1}+x=0,-{{\rm e}^{\int ^{{\frac {1}{ \left ( {a}^{2}-1 \right ) y \left ( x \right ) } \left ( -{a}^{2}x+\sqrt { \left ( {a}^{2}-1 \right ) \left ( y \left ( x \right ) \right ) ^{2}+{a}^{2}{x}^{2}} \right ) }}\!{a \left ( a\sqrt {{{\it \_a}}^{2}+1}-{\it \_a} \right ) {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \left ( {\it \_a}\,a-\sqrt {{{\it \_a}}^{2}+1} \right ) ^{-1} \left ( {{\it \_a}}^{2}a-\sqrt {{{\it \_a}}^{2}+1}{\it \_a}+a \right ) ^{-1}}{d{\it \_a}}}}{\it \_C1}+x=0 \right \} \]