\[ x y'(x)^2+(y(x)-3 x) y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 2.02653 (sec), leaf count = 383
DSolve[y[x] + (-3*x + y[x])*Derivative[1][y][x] + x*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {1}{8} \left (-\sqrt {\frac {\frac {y(x)}{x}-9}{\frac {y(x)}{x}-1}} \left (\frac {y(x)}{x}-1\right )+\sqrt {\frac {y(x)}{x}-9} \sqrt {\frac {y(x)}{x}-1}-3 \log \left (\frac {y(x)}{x}\right )-\frac {10 \sqrt {\frac {y(x)}{x}-9} \sin ^{-1}\left (\frac {\sqrt {9-\frac {y(x)}{x}}}{2 \sqrt {2}}\right )}{\sqrt {9-\frac {y(x)}{x}}}+6 \tanh ^{-1}\left (\frac {1}{3} \sqrt {\frac {\frac {y(x)}{x}-9}{\frac {y(x)}{x}-1}}\right )+8 \tanh ^{-1}\left (\sqrt {\frac {\frac {y(x)}{x}-9}{\frac {y(x)}{x}-1}}\right )\right )=\frac {\log (x)}{2}+c_1,y(x)\right ],\text {Solve}\left [\frac {1}{8} \left (-\sqrt {\frac {\frac {y(x)}{x}-9}{\frac {y(x)}{x}-1}} \left (\frac {y(x)}{x}-1\right )+\sqrt {\frac {y(x)}{x}-9} \sqrt {\frac {y(x)}{x}-1}+3 \log \left (\frac {y(x)}{x}\right )-\frac {10 \sqrt {\frac {y(x)}{x}-9} \sin ^{-1}\left (\frac {\sqrt {9-\frac {y(x)}{x}}}{2 \sqrt {2}}\right )}{\sqrt {9-\frac {y(x)}{x}}}+6 \tanh ^{-1}\left (\frac {1}{3} \sqrt {\frac {\frac {y(x)}{x}-9}{\frac {y(x)}{x}-1}}\right )+8 \tanh ^{-1}\left (\sqrt {\frac {\frac {y(x)}{x}-9}{\frac {y(x)}{x}-1}}\right )\right )=-\frac {\log (x)}{2}+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.068 (sec), leaf count = 136
dsolve(x*diff(y(x),x)^2+(y(x)-3*x)*diff(y(x),x)+y(x) = 0,y(x))
\[y \left (x \right ) = x\]