# On a substitution to solve a high order differential equation (exercise).

I have solved Linear first order differential equations, I know how to separate variables, for higher orders I know the the substitutions that apply to the bernoulli equation and homogeneous equations.

$$y^{(4)}+ 4y^{(2)}+4y = cos2t - sin2t$$
I am given a hint that : $$r^4+4r^2 + 4r^0 = 0 \implies (r^2+2)^2 = 0 \implies r = \pm i \sqrt{2}$$
Could I have a reference to how to solve these kind of differential equations? Or am I just missing a trick that makes this a first order? I tried thinking about substituting Eulers formula in the left hand side but I am missing an $i$.
hint: use the fact that $e^{i\sqrt{2}t}=\cos(\sqrt{2}t)+i\sin(\sqrt{2}t)$