\[ a x \sqrt {y'(x)^2+1}+x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.91211 (sec), leaf count = 327
\[\left \{\text {Solve}\left [\frac {2 i \tan ^{-1}\left (\frac {y(x)}{x \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \tanh ^{-1}\left (\frac {-a^2-\frac {i y(x)}{x}+1}{a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )-a \tanh ^{-1}\left (\frac {-a^2+\frac {i y(x)}{x}+1}{a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \log \left (\frac {y(x)^2}{x^2}+1\right )}{2 a^2-2}=\frac {a \log \left (x-a^2 x\right )}{1-a^2}+c_1,y(x)\right ],\text {Solve}\left [\frac {-2 i \tan ^{-1}\left (\frac {y(x)}{x \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )-a \tanh ^{-1}\left (\frac {-a^2-\frac {i y(x)}{x}+1}{a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \tanh ^{-1}\left (\frac {-a^2+\frac {i y(x)}{x}+1}{a \sqrt {a^2-\frac {y(x)^2}{x^2}-1}}\right )+a \log \left (\frac {y(x)^2}{x^2}+1\right )}{2 a^2-2}=\frac {a \log \left (x-a^2 x\right )}{1-a^2}+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.386 (sec), leaf count = 223
\[x -\frac {{\mathrm e}^{\frac {\arcsinh \left (\frac {\sqrt {-a^{2} x^{2}+x^{2}+y \relax (x )^{2}}\, a +y \relax (x )}{\left (a^{2}-1\right ) x}\right )}{a}} c_{1}}{\sqrt {\frac {-a^{2} x^{2}+a^{2} y \relax (x )^{2}+2 \sqrt {-a^{2} x^{2}+x^{2}+y \relax (x )^{2}}\, a y \relax (x )+x^{2}+y \relax (x )^{2}}{\left (a^{2}-1\right )^{2} x^{2}}}} = 0\]