\[ 2 \left (2 a+4 x^2-1\right ) y'(x)-8 a x y(x)+y^{(3)}(x)-6 x y''(x)=0 \] ✓ Mathematica : cpu = 0.0546179 (sec), leaf count = 57
DSolve[-8*a*x*y[x] + 2*(-1 + 2*a + 4*x^2)*Derivative[1][y][x] - 6*x*Derivative[2][y][x] + Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 H_{\frac {a}{2}}(x) \, _1F_1\left (-\frac {a}{4};\frac {1}{2};x^2\right )+c_1 H_{\frac {a}{2}}(x){}^2+c_3 \, _1F_1\left (-\frac {a}{4};\frac {1}{2};x^2\right ){}^2\right \}\right \}\] ✓ Maple : cpu = 0.094 (sec), leaf count = 59
dsolve(diff(diff(diff(y(x),x),x),x)-6*x*diff(diff(y(x),x),x)+2*(4*x^2+2*a-1)*diff(y(x),x)-8*a*x*y(x)=0,y(x))
\[y \left (x \right ) = x^{2} \left (\KummerU \left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right )^{2} c_{2}+\KummerU \left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) \KummerM \left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) c_{3}+\KummerM \left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right )^{2} c_{1}\right )\]