\[ x y'(x)^2+(y(x)-3 x) y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 0.310441 (sec), leaf count = 1493
DSolve[y[x] + (-3*x + y[x])*Derivative[1][y][x] + x*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {6912 e^{4 c_1}-\frac {4 e^{8 c_1}}{x^2}}{384 \sqrt [3]{373248 e^{4 c_1} x-\frac {4320 e^{8 c_1}}{x}+\frac {48 \sqrt {6} \sqrt {10077696 e^{8 c_1} x^6+139968 e^{12 c_1} x^4+648 e^{16 c_1} x^2+e^{20 c_1}}}{x^2}-\frac {e^{12 c_1}}{x^3}}}+\frac {1}{96} \sqrt [3]{373248 e^{4 c_1} x-\frac {4320 e^{8 c_1}}{x}+\frac {48 \sqrt {6} \sqrt {10077696 e^{8 c_1} x^6+139968 e^{12 c_1} x^4+648 e^{16 c_1} x^2+e^{20 c_1}}}{x^2}-\frac {e^{12 c_1}}{x^3}}-\frac {e^{4 c_1}}{96 x}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \left (6912 e^{4 c_1}-\frac {4 e^{8 c_1}}{x^2}\right )}{768 \sqrt [3]{373248 e^{4 c_1} x-\frac {4320 e^{8 c_1}}{x}+\frac {48 \sqrt {6} \sqrt {10077696 e^{8 c_1} x^6+139968 e^{12 c_1} x^4+648 e^{16 c_1} x^2+e^{20 c_1}}}{x^2}-\frac {e^{12 c_1}}{x^3}}}-\frac {1}{192} \left (1-i \sqrt {3}\right ) \sqrt [3]{373248 e^{4 c_1} x-\frac {4320 e^{8 c_1}}{x}+\frac {48 \sqrt {6} \sqrt {10077696 e^{8 c_1} x^6+139968 e^{12 c_1} x^4+648 e^{16 c_1} x^2+e^{20 c_1}}}{x^2}-\frac {e^{12 c_1}}{x^3}}-\frac {e^{4 c_1}}{96 x}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \left (6912 e^{4 c_1}-\frac {4 e^{8 c_1}}{x^2}\right )}{768 \sqrt [3]{373248 e^{4 c_1} x-\frac {4320 e^{8 c_1}}{x}+\frac {48 \sqrt {6} \sqrt {10077696 e^{8 c_1} x^6+139968 e^{12 c_1} x^4+648 e^{16 c_1} x^2+e^{20 c_1}}}{x^2}-\frac {e^{12 c_1}}{x^3}}}-\frac {1}{192} \left (1+i \sqrt {3}\right ) \sqrt [3]{373248 e^{4 c_1} x-\frac {4320 e^{8 c_1}}{x}+\frac {48 \sqrt {6} \sqrt {10077696 e^{8 c_1} x^6+139968 e^{12 c_1} x^4+648 e^{16 c_1} x^2+e^{20 c_1}}}{x^2}-\frac {e^{12 c_1}}{x^3}}-\frac {e^{4 c_1}}{96 x}\right \},\left \{y(x)\to -\frac {e^{-8 c_1} \left (108 e^{12 c_1}-\frac {4 e^{8 c_1}}{x^2}\right )}{3 \sqrt [3]{729 e^{20 c_1} x-\frac {540 e^{16 c_1}}{x}+\frac {3 \sqrt {3} \sqrt {19683 e^{40 c_1} x^6+17496 e^{36 c_1} x^4+5184 e^{32 c_1} x^2+512 e^{28 c_1}}}{x^2}-\frac {8 e^{12 c_1}}{x^3}}}+\frac {1}{3} e^{-8 c_1} \sqrt [3]{729 e^{20 c_1} x-\frac {540 e^{16 c_1}}{x}+\frac {3 \sqrt {3} \sqrt {19683 e^{40 c_1} x^6+17496 e^{36 c_1} x^4+5184 e^{32 c_1} x^2+512 e^{28 c_1}}}{x^2}-\frac {8 e^{12 c_1}}{x^3}}-\frac {2 e^{-4 c_1}}{3 x}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) e^{-8 c_1} \left (108 e^{12 c_1}-\frac {4 e^{8 c_1}}{x^2}\right )}{6 \sqrt [3]{729 e^{20 c_1} x-\frac {540 e^{16 c_1}}{x}+\frac {3 \sqrt {3} \sqrt {19683 e^{40 c_1} x^6+17496 e^{36 c_1} x^4+5184 e^{32 c_1} x^2+512 e^{28 c_1}}}{x^2}-\frac {8 e^{12 c_1}}{x^3}}}-\frac {1}{6} \left (1-i \sqrt {3}\right ) e^{-8 c_1} \sqrt [3]{729 e^{20 c_1} x-\frac {540 e^{16 c_1}}{x}+\frac {3 \sqrt {3} \sqrt {19683 e^{40 c_1} x^6+17496 e^{36 c_1} x^4+5184 e^{32 c_1} x^2+512 e^{28 c_1}}}{x^2}-\frac {8 e^{12 c_1}}{x^3}}-\frac {2 e^{-4 c_1}}{3 x}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) e^{-8 c_1} \left (108 e^{12 c_1}-\frac {4 e^{8 c_1}}{x^2}\right )}{6 \sqrt [3]{729 e^{20 c_1} x-\frac {540 e^{16 c_1}}{x}+\frac {3 \sqrt {3} \sqrt {19683 e^{40 c_1} x^6+17496 e^{36 c_1} x^4+5184 e^{32 c_1} x^2+512 e^{28 c_1}}}{x^2}-\frac {8 e^{12 c_1}}{x^3}}}-\frac {1}{6} \left (1+i \sqrt {3}\right ) e^{-8 c_1} \sqrt [3]{729 e^{20 c_1} x-\frac {540 e^{16 c_1}}{x}+\frac {3 \sqrt {3} \sqrt {19683 e^{40 c_1} x^6+17496 e^{36 c_1} x^4+5184 e^{32 c_1} x^2+512 e^{28 c_1}}}{x^2}-\frac {8 e^{12 c_1}}{x^3}}-\frac {2 e^{-4 c_1}}{3 x}\right \}\right \}\] ✓ Maple : cpu = 0.29 (sec), leaf count = 136
dsolve(x*diff(y(x),x)^2+(y(x)-3*x)*diff(y(x),x)+y(x) = 0,y(x))
\[y \left (x \right ) = x\]