syms y(t)
Dy = diff(y);
DDy = diff(y,t,2);
DDDy = diff(y,t,3);
y(t) = dsolve(diff(y, t, 4) == -6*DDDy -14*DDy - 16*Dy -8*y+24, y(0) == 2, Dy(0) == -2, DDy(0) == 2, DDDy(0) == -2);
y(t) = simplify(y)