\[ x^{2 c-2} y'(x)+(c-1) x^{2 c-3} y(x)+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0247922 (sec), leaf count = 183
DSolve[(-1 + c)*x^(-3 + 2*c)*y[x] + x^(-2 + 2*c)*Derivative[1][y][x] + Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \, _1F_2\left (\frac {1}{2}-\frac {1}{2 c};1-\frac {1}{c},1-\frac {1}{2 c};-\frac {x^{2 c}}{4 c^2}\right )+4^{-1/c} c^{-2/c} c_3 \left (x^{2 c}\right )^{\frac {1}{c}} \, _1F_2\left (\frac {1}{2}+\frac {1}{2 c};1+\frac {1}{2 c},1+\frac {1}{c};-\frac {x^{2 c}}{4 c^2}\right )+2^{-1/c} c^{-1/c} c_2 \left (x^{2 c}\right )^{\left .\frac {1}{2}\right /c} \, _1F_2\left (\frac {1}{2};1-\frac {1}{2 c},1+\frac {1}{2 c};-\frac {x^{2 c}}{4 c^2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.07 (sec), leaf count = 73
dsolve(diff(diff(diff(y(x),x),x),x)+x^(2*c-2)*diff(y(x),x)+(c-1)*x^(2*c-3)*y(x)=0,y(x))
\[y \left (x \right ) = x \left (\BesselY \left (\frac {1}{2 c}, \frac {x^{c}}{2 c}\right )^{2} c_{2}+\BesselY \left (\frac {1}{2 c}, \frac {x^{c}}{2 c}\right ) \BesselJ \left (\frac {1}{2 c}, \frac {x^{c}}{2 c}\right ) c_{3}+\BesselJ \left (\frac {1}{2 c}, \frac {x^{c}}{2 c}\right )^{2} c_{1}\right )\]