Answer:
Step-by-step explanation:
The equation is a<em> </em><em>linear differential equation: y⁽⁴⁾- y = 0 </em>
We assume the form of the solution y(t) is
where are the roots of the auxiliary equation.
So, use the auxiliary equation: to find the roots; the values are : α₁ = 1, α₂ = -1, α₃ = i, α₄ = -i
Then inserting values in the assumed solution
⇒ <em></em>
Also, because the last 2 terms have complex power, the solution can be written with cosine and sine terms:
<em>Using the Euler's formula: , we can rewrite the solution as:</em>
=
<em>Where: </em>
<em>Finally the solution for de linear differential equation y^(4) - y =0 is:</em>
<em> </em>