\[ \left (-\nu ^2+x^2-2 x+\frac {1}{4}\right ) y'(x)+\left (\nu ^2-\frac {1}{4}\right ) y(x)+x^2 y^{(3)}(x)-2 \left (x^2-x\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.157331 (sec), leaf count = 86
DSolve[(-1/4 + nu^2)*y[x] + (1/4 - nu^2 - 2*x + x^2)*Derivative[1][y][x] - 2*(-x + x^2)*Derivative[2][y][x] + x^2*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_3 e^x x^{\nu +\frac {1}{2}} \Gamma \left (\nu +\frac {1}{2}\right ) \, _1\tilde {F}_1\left (\nu +\frac {1}{2};2 \nu +1;-x\right )}{\Gamma \left (\frac {3}{2}-\nu \right )}+c_2 e^x G_{2,3}^{2,1}\left (x\left |\begin {array}{c} 1,0 \\ \frac {1}{2}-\nu ,\nu +\frac {1}{2},0 \\\end {array}\right .\right )+c_1 e^x\right \}\right \}\] ✓ Maple : cpu = 0.168 (sec), leaf count = 37
dsolve(x^2*diff(diff(diff(y(x),x),x),x)-2*(x^2-x)*diff(diff(y(x),x),x)+(x^2-2*x+1/4-nu^2)*diff(y(x),x)+(nu^2-1/4)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{\frac {x}{2}} \sqrt {x}\, \BesselI \left (\nu , \frac {x}{2}\right )+c_{3} {\mathrm e}^{\frac {x}{2}} \sqrt {x}\, \BesselK \left (\nu , \frac {x}{2}\right )\]