Q1E Find a general solution for the ... [FREE SOLUTION]

91影视

Fundamentals Of Differential Equations And Boundary Value Problems

R. Kent Nagle, Edward B. Saff, Arthur David Snider

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 616 pages

ISBN: 9780321977069

Chapter 6: Q1E (page 332)

Find a general solution for the differential equation with x as the independent variable.
$y''' + 2 y'' - 8 y' = 0$

Short Answer

Expert verified

Thus, the general solution to the given differential equation is. $y = C_{1} + C_{2} e^{- 4 x} + C_{3} e^{2 x}$

Step by step solution

Use the given equation to find a general solution for the differential equation with x

The given differential equation is,

$y''' + 2 y'' - 8 y' = 0$

The auxiliary equation is. $m^{3} + 2 m^{2} - 8 m = 0$

Find the roots of the auxiliary equation.

$\begin{matrix} m^{3} + 2 m^{2} - 8 m = 0 \\ m (m^{2} + 2 m - 8) = 0 \\ m (m + 4) (m - 2) = 0 \\ m_{1} = 0, m_{2} = 鈭� 4, m_{3} = 2 \end{matrix}$

General solution.

The roots are real and distinct; therefore the general solution to the given differential equation is given as:

$\begin{matrix} y = C_{1} e^{m_{1} x} + C_{2} e^{m_{2} x} + C_{3} e^{m_{3} x} \\ y = C_{1} e^{(0) x} + C_{2} e^{(- 4) x} + C_{3} e^{(2) x} \\ y = C_{1} + C_{2} e^{- 4 x} + C_{3} e^{2 x} \end{matrix}$

Thus, the general solution to the given differential equation is. $y = C_{1} + C_{2} e^{- 4 x} + C_{3} e^{2 x}$

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91影视

Find a general solution for the differential equation with x as the independent variable.
$y''' + 2 y'' - 8 y' = 0$

Short Answer

Step by step solution

Use the given equation to find a general solution for the differential equation with x

General solution.

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91影视

Find a general solution for the differential equation with x as the independent variable.y'''+2y''-8y'=0

Short Answer

Step by step solution

Use the given equation to find a general solution for the differential equation with x

General solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Pure Maths

Probability and Statistics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find a general solution for the differential equation with x as the independent variable.
$y''' + 2 y'' - 8 y' = 0$