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Now need to find the homogenous solution. Well, if the root was real, it would be easier but now I'm stuck and don't know how to proceed.

What am I supposed to do to solve this ?

Equation is : d

^{4}y(t)/dt

^{4}+6d

^{3}y(t)/dt

^{3}+ 22d

^{2}y(t)/dt

^{2}+ 30dy(t)/dt + 13y(t) = f(t)

Just need to solve the homogenous part so f(t) is just a dummy function