# Find the largest constant r so that \phi \left( x \right) = {e^{rx}} is a solution to y''' - 2y''...

## Question:

Find the largest constant {eq}r {/eq} so that {eq}\phi \left( x \right) = {e^{rx}} {/eq} is a solution to {eq}y''' - 2y'' - y + 2y = 0 {/eq}.

a. -5

b. 1

c. 2

d. 7/2

e. 4

## Third Order Differential Equation:

A third order differential equation is the differential equation where the highest derivative that appears is the third derivative of the function. The third order homogeneous differential equation has three independent functions in its solution set.

Become a Study.com member to unlock this answer!

Given:

$$y''' -2y'' -y'+2y=0\\$$

Calculate the solution of the given homogeneous equation.

\begin{align} y''' -2y'' -y'+2y &= 0 && ...