\[ -(2 v+x) y''(x)-(-2 v+x-1) y'(x)+x y^{(3)}(x)+(x-1) y(x)=0 \] ✓ Mathematica : cpu = 0.172087 (sec), leaf count = 93
\[\left \{\left \{y(x)\to \frac {c_3 e^x x^{2 v+2} \Gamma \left (v+\frac {3}{2}\right ) \, _1\tilde {F}_1\left (v+\frac {3}{2};2 v+3;-2 x\right )}{\Gamma \left (\frac {1}{2}-v\right )}+c_2 2^{-2 v-2} e^x G_{2,3}^{2,1}\left (2 x\left |\begin {array}{c} 1,v+\frac {3}{2} \\ 1,2 (v+1),0 \\\end {array}\right .\right )+c_1 e^x\right \}\right \}\] ✓ Maple : cpu = 0.186 (sec), leaf count = 35
\[y \relax (x ) = {\mathrm e}^{x} c_{1}+c_{2} x^{v +1} \BesselI \left (-v -1, x\right )+c_{3} x^{v +1} \BesselK \left (v +1, x\right )\]