\[ -2 \left (\nu ^2 x^2+6\right ) y''(x)+\nu ^2 \left (\nu ^2 x^2+4\right ) y(x)+x^2 y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.289472 (sec), leaf count = 110
DSolve[nu^2*(4 + nu^2*x^2)*y[x] - 2*(6 + nu^2*x^2)*Derivative[2][y][x] + x^2*Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_3 (1-x) e^{-\nu x} \left (\nu ^2 x^2+\nu ^2 x+\nu ^2+6 \nu x+6 \nu +15\right )}{x}+\frac {c_4 (1-x) e^{\nu x} \left (\nu ^2 x^2+\nu ^2 x+\nu ^2-6 \nu x-6 \nu +15\right )}{x}+\frac {c_1 e^{-\nu x}}{x}+\frac {c_2 e^{\nu x}}{x}\right \}\right \}\] ✓ Maple : cpu = 0.203 (sec), leaf count = 62
dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x)-2*(nu^2*x^2+6)*diff(diff(y(x),x),x)+nu^2*(nu^2*x^2+4)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {\left (\nu ^{2} x^{3} c_{4}+6 \nu \,x^{2} c_{4}+15 x c_{4}+c_{2}\right ) {\mathrm e}^{-\nu x}+{\mathrm e}^{\nu x} \left (\nu ^{2} x^{3} c_{3}-6 \nu \,x^{2} c_{3}+15 x c_{3}+c_{1}\right )}{x}\]