\[ \boxed { x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a=0} \]
Mathematica: cpu = 0.374047 (sec), leaf count = 430 \[ \left \{\left \{y(x)\to -\frac {8 a^2}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}-\frac {\sqrt {16 a^3 \sinh \left (c_1\right )+16 a^3 \cosh \left (c_1\right )-8 a^2 x \sinh \left (c_1\right )-8 a^2 x \cosh \left (c_1\right )-8 a^2 \sinh \left (2 c_1\right )-8 a^2 \cosh \left (2 c_1\right )+a x^2 \sinh \left (c_1\right )+a x^2 \cosh \left (c_1\right )+2 a x \sinh \left (2 c_1\right )+2 a x \cosh \left (2 c_1\right )+a \sinh \left (3 c_1\right )+a \cosh \left (3 c_1\right )}}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}-\frac {2 a x}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}+\frac {2 a \sinh \left (c_1\right )}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}+\frac {2 a \cosh \left (c_1\right )}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}\right \},\left \{y(x)\to -\frac {8 a^2}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}+\frac {\sqrt {16 a^3 \sinh \left (c_1\right )+16 a^3 \cosh \left (c_1\right )-8 a^2 x \sinh \left (c_1\right )-8 a^2 x \cosh \left (c_1\right )-8 a^2 \sinh \left (2 c_1\right )-8 a^2 \cosh \left (2 c_1\right )+a x^2 \sinh \left (c_1\right )+a x^2 \cosh \left (c_1\right )+2 a x \sinh \left (2 c_1\right )+2 a x \cosh \left (2 c_1\right )+a \sinh \left (3 c_1\right )+a \cosh \left (3 c_1\right )}}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}-\frac {2 a x}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}+\frac {2 a \sinh \left (c_1\right )}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}+\frac {2 a \cosh \left (c_1\right )}{4 a-\sinh \left (c_1\right )-\cosh \left (c_1\right )}\right \}\right \} \]
Maple: cpu = 0.484 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) =-2\,\sqrt {ax},y \left ( x \right ) =2\, \sqrt {ax},y \left ( x \right ) ={\it \_C1}\,x+{\frac {a}{{\it \_C1}}} \right \} \]