\[ \boxed { ax{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +b{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +cy \left ( x \right ) =0} \]
Mathematica: cpu = 0.049006 (sec), leaf count = 190 \[ \left \{\left \{y(x)\to c_1 a^{\frac {1}{2} \left (\frac {b}{a}-1\right )} c^{\frac {1}{2} \left (1-\frac {b}{a}\right )} x^{\frac {1}{2} \left (1-\frac {b}{a}\right )} \Gamma \left (\frac {b}{a}\right ) J_{\frac {b}{a}-1}\left (\frac {2 \sqrt {c} \sqrt {x}}{\sqrt {a}}\right )+c_2 a^{\frac {1}{2} \left (1-\frac {b}{a}\right )-\frac {a-b}{a}} c^{\frac {a-b}{a}+\frac {1}{2} \left (\frac {b}{a}-1\right )} x^{\frac {a-b}{a}+\frac {1}{2} \left (\frac {b}{a}-1\right )} \Gamma \left (2-\frac {b}{a}\right ) J_{1-\frac {b}{a}}\left (\frac {2 \sqrt {c} \sqrt {x}}{\sqrt {a}}\right )\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 77 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {a-b}{2\,a}}}{ {\sl J}_{{\frac {-a+b}{a}}}\left (2\,\sqrt {{\frac {c}{a}}}\sqrt {x} \right )}+{\it \_C2}\,{x}^{{\frac {a-b}{2\,a}}}{{\sl Y}_{{\frac {-a+b}{ a}}}\left (2\,\sqrt {{\frac {c}{a}}}\sqrt {x}\right )} \right \} \]