\[ \boxed { y \left ( x \right ) \sqrt { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1}-ay \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -ax=0} \]
Mathematica: cpu = 0.351045 (sec), leaf count = 212 \[ \left \{\left \{y(x)\to -\frac {\sqrt {a^6 \left (-x^2\right )+3 a^4 x^2+2 a^2 x e^{a^2 c_1-c_1}-2 x e^{a^2 c_1-c_1}+e^{2 a^2 c_1-2 c_1}-3 a^2 x^2+x^2}}{\sqrt {a^6-3 a^4+3 a^2-1}}\right \},\left \{y(x)\to \frac {\sqrt {a^6 \left (-x^2\right )+3 a^4 x^2+2 a^2 x e^{a^2 c_1-c_1}-2 x e^{a^2 c_1-c_1}+e^{2 a^2 c_1-2 c_1}-3 a^2 x^2+x^2}}{\sqrt {a^6-3 a^4+3 a^2-1}}\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 223 \[ \left \{ x-{{\rm e}^{\int ^{{\frac {1}{ \left ( {a}^{2}-1 \right ) y \left ( x \right ) } \left ( -{a}^{2}x+\sqrt {{a}^{2}{x}^{2}+{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}- \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}\!{a \left ( a\sqrt {{{\it \_a}}^{2}+1}-{\it \_a} \right ) {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \left ( -{\it \_a} \,a+\sqrt {{{\it \_a}}^{2}+1} \right ) ^{-1} \left ( -{{\it \_a}}^{2}a+ \sqrt {{{\it \_a}}^{2}+1}{\it \_a}-a \right ) ^{-1}}{d{\it \_a}}}}{\it \_C1}=0,x-{{\rm e}^{\int ^{-{\frac {1}{ \left ( {a}^{2}-1 \right ) y \left ( x \right ) } \left ( {a}^{2}x+\sqrt {{a}^{2}{x}^{2}+{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}- \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}\!{a \left ( a\sqrt {{{\it \_a}}^{2}+1}-{\it \_a} \right ) {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \left ( -{\it \_a} \,a+\sqrt {{{\it \_a}}^{2}+1} \right ) ^{-1} \left ( -{{\it \_a}}^{2}a+ \sqrt {{{\it \_a}}^{2}+1}{\it \_a}-a \right ) ^{-1}}{d{\it \_a}}}}{\it \_C1}=0 \right \} \]