\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +{x}^{2\,c-2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( c-1 \right ) {x}^{2\,c-3}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.034004 (sec), leaf count = 183 \[ \left \{\left \{y(x)\to c_1 \, _1F_2\left (\frac {1}{2}-\frac {1}{2 c};1-\frac {1}{c},1-\frac {1}{2 c};-\frac {x^{2 c}}{4 c^2}\right )+4^{-1/c} c_3 c^{-2/c} \left (x^{2 c}\right )^{\frac {1}{c}} \, _1F_2\left (\frac {1}{2}+\frac {1}{2 c};1+\frac {1}{2 c},1+\frac {1}{c};-\frac {x^{2 c}}{4 c^2}\right )+2^{-1/c} c_2 c^{-1/c} \left (x^{2 c}\right )^{\left .\frac {1}{2}\right /c} \, _1F_2\left (\frac {1}{2};1-\frac {1}{2 c},1+\frac {1}{2 c};-\frac {x^{2 c}}{4 c^2}\right )\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 74 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,x \left ( {{\sl J}_{{\frac {1 }{2\,c}}}\left ({\frac {{x}^{c}}{2\,c}}\right )} \right ) ^{2}+{\it \_C2} \,x \left ( {{\sl Y}_{{\frac {1}{2\,c}}}\left ({\frac {{x}^{c}}{2\,c}} \right )} \right ) ^{2}+{\it \_C3}\,x{{\sl J}_{{\frac {1}{2\,c}}}\left ({ \frac {{x}^{c}}{2\,c}}\right )}{{\sl Y}_{{\frac {1}{2\,c}}}\left ({ \frac {{x}^{c}}{2\,c}}\right )} \right \} \]