\[ a+x y'(x)^2-y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.857251 (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 = 0.162 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\frac {{{\it \_C1}}^{2}x+a}{{\it \_C1}}},y \left ( x \right ) =-2\,\sqrt {ax},y \left ( x \right ) =2\,\sqrt {ax} \right \} \]