Find the general solution to:
y^(4) - y =0

Step-by-step explanation:

The equation is a linear differential equation: y⁽⁴⁾- y = 0

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

⇒

Also, because the last 2 terms have complex power, the solution can be written with cosine and sine terms:

Using the Euler's formula: , we can rewrite the solution as:

 =

Where:

Finally the solution for de linear differential equation y^(4) - y =0 is:

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.