\[ \boxed { \left ( 3\,x+5 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}- \left ( 3\,y \left ( x \right ) +x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) =0} \]
Mathematica: cpu = 0.634581 (sec), leaf count = 479 \[ \left \{\left \{y(x)\to \frac {-\sqrt {5} \sqrt {-144 e^{\frac {4 c_1}{3}} x^2-360 e^{\frac {4 c_1}{3}} x+24 e^{\frac {8 c_1}{3}} x-225 e^{\frac {4 c_1}{3}}+30 e^{\frac {8 c_1}{3}}-e^{4 c_1}}+6 e^{\frac {4 c_1}{3}} x+15 e^{\frac {4 c_1}{3}}-30 x-25}{18 \left (e^{\frac {4 c_1}{3}}+5\right )}\right \},\left \{y(x)\to \frac {\sqrt {5} \sqrt {-144 e^{\frac {4 c_1}{3}} x^2-360 e^{\frac {4 c_1}{3}} x+24 e^{\frac {8 c_1}{3}} x-225 e^{\frac {4 c_1}{3}}+30 e^{\frac {8 c_1}{3}}-e^{4 c_1}}+6 e^{\frac {4 c_1}{3}} x+15 e^{\frac {4 c_1}{3}}-30 x-25}{18 \left (e^{\frac {4 c_1}{3}}+5\right )}\right \},\left \{y(x)\to \frac {-\sqrt {5} \sqrt {144 e^{\frac {4 c_1}{3}} x^2+360 e^{\frac {4 c_1}{3}} x+24 e^{\frac {8 c_1}{3}} x+225 e^{\frac {4 c_1}{3}}+30 e^{\frac {8 c_1}{3}}+e^{4 c_1}}+6 e^{\frac {4 c_1}{3}} x+15 e^{\frac {4 c_1}{3}}+30 x+25}{18 \left (e^{\frac {4 c_1}{3}}-5\right )}\right \},\left \{y(x)\to \frac {\sqrt {5} \sqrt {144 e^{\frac {4 c_1}{3}} x^2+360 e^{\frac {4 c_1}{3}} x+24 e^{\frac {8 c_1}{3}} x+225 e^{\frac {4 c_1}{3}}+30 e^{\frac {8 c_1}{3}}+e^{4 c_1}}+6 e^{\frac {4 c_1}{3}} x+15 e^{\frac {4 c_1}{3}}+30 x+25}{18 \left (e^{\frac {4 c_1}{3}}-5\right )}\right \}\right \} \]
Maple: cpu = 0.452 (sec), leaf count = 67 \[ \left \{ y \left ( x \right ) ={\frac { \left ( -3\,{{\it \_C1}}^{2}+{ \it \_C1} \right ) x}{-3\,{\it \_C1}+1}}-5\,{\frac {{{\it \_C1}}^{2}}{- 3\,{\it \_C1}+1}},y \left ( x \right ) ={\frac {x}{3}}+{\frac {10}{9}}-{ \frac {2}{9}\sqrt {15\,x+25}},y \left ( x \right ) ={\frac {x}{3}}+{ \frac {10}{9}}+{\frac {2}{9}\sqrt {15\,x+25}} \right \} \]