\[ (a+b) y''(x)-a y(x)+x y^{(3)}(x)-x y'(x)=0 \] ✓ Mathematica : cpu = 0.107786 (sec), leaf count = 153
DSolve[-(a*y[x]) - x*Derivative[1][y][x] + (a + b)*Derivative[2][y][x] + x*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{2} i c_2 x \, _1F_2\left (\frac {a}{2}+\frac {1}{2};\frac {3}{2},\frac {a}{2}+\frac {b}{2}+\frac {1}{2};\frac {x^2}{4}\right )+c_1 \, _1F_2\left (\frac {a}{2};\frac {1}{2},\frac {a}{2}+\frac {b}{2};\frac {x^2}{4}\right )+c_3 \left (\frac {i}{2}\right )^{-a-b+2} x^{-a-b+2} \, _1F_2\left (1-\frac {b}{2};-\frac {a}{2}-\frac {b}{2}+\frac {3}{2},-\frac {a}{2}-\frac {b}{2}+2;\frac {x^2}{4}\right )\right \}\right \}\] ✓ Maple : cpu = 0.175 (sec), leaf count = 92
dsolve(x*diff(diff(diff(y(x),x),x),x)+(a+b)*diff(diff(y(x),x),x)-x*diff(y(x),x)-a*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \hypergeom \left (\left [\frac {a}{2}\right ], \left [\frac {1}{2}, \frac {a}{2}+\frac {b}{2}\right ], \frac {x^{2}}{4}\right )+c_{2} x \hypergeom \left (\left [\frac {1}{2}+\frac {a}{2}\right ], \left [\frac {3}{2}, \frac {a}{2}+\frac {b}{2}+\frac {1}{2}\right ], \frac {x^{2}}{4}\right )+c_{3} x^{-a -b +2} \hypergeom \left (\left [1-\frac {b}{2}\right ], \left [2-\frac {b}{2}-\frac {a}{2}, -\frac {a}{2}-\frac {b}{2}+\frac {3}{2}\right ], \frac {x^{2}}{4}\right )\]