Determine whether the function is a solution of the differential equation
y''' - 8y = 0
(a) y = cos(2x)
(b) y = e^(2x)
What exactly is one suppose to do here? Is this suppose to be the third degree because we only covered first degree DE?
Determine whether the function is a solution of the differential equation
y''' - 8y = 0
(a) y = cos(2x)
(b) y = e^(2x)
What exactly is one suppose to do here? Is this suppose to be the third degree because we only covered first degree DE?
$\displaystyle y'''$ means the third derivative. You are suppose to use the solutions in a) and b) and plug them in the original DEQ. If $\displaystyle y$ from a) or b) satisfies $\displaystyle y''' + 8y =0$ then it is a solution to the DEQ.
From a)
$\displaystyle y''' = 8\cos(2x)$
and so
$\displaystyle 8\cos(2x) - 8cos(2x) = 0$
So, a) is a solution to the DEQ. Now, check if b) works.