✓ Mathematica : cpu = 1.03295 (sec), leaf count = 230
DSolve[(3 - 12*n^2 - 4*x^4)*y[x] + (-3 + 12*n^2)*x*Derivative[1][y][x] - (3 + 4*n^2)*x^2*Derivative[2][y][x] + 4*x^3*Derivative[3][y][x] + x^4*Derivative[4][y][x] == 0,y[x],x]
✓ Maple : cpu = 0.279 (sec), leaf count = 88
dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+4*x^3*diff(diff(diff(y(x),x),x),x)-(4*n^2+3)*x^2*diff(diff(y(x),x),x)+(12*n^2-3)*x*diff(y(x),x)-(4*x^4+12*n^2-3)*y(x)=0,y(x))