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