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


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.

Answer and Explanation:

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

Calculate the solution of the given homogeneous equation.

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

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Learn more about this topic:

Separable Differential Equation: Definition & Examples


Chapter 16 / Lesson 1

Discover what separable differential equations are and their uses. Learn to identify if an equation is separable and how to solve them through given examples.

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