Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

Answers without the blur.

Just sign up for free and you're in.

Short Answer

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

The general solution for the differential equation with x as the independent variableis . $y (x) = c_{1} e^{- x} + c_{2} e^{- 5 x} + c_{3} e^{4 x}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Auxiliary equation:

The given differential equationis $y''' - y'' + 2 y = 0$ . To solve this equation, we look at its auxiliary equation which is $m^{3} - m^{2} + 2 = 0$ . Observe that -1 is a solution of this equation. So,

$m^{3} - m^{2} + 2 = (m + 1) (m^{2} - 2 m + 2)$

Step 2: Inspecting the sum further:

To get the other two roots of auxillary equation, we need to solve $m^{3} - m^{2} + 2 = 0$ . We have,

$m = \frac{2 \pm \sqrt{4 - 8}}{2} = 1 \pm i$

Step 3: General solution:

We have m = -1, $1 \pm i$ .From (7) of 328 and (18) of page 330, we conclude that the general solution of the given differential equation is $y = C_{1} e^{- x} + C_{2} e^{x} \cos x + C_{3} e^{x} \sin x$ where $C_{1}, C_{2}, C_{3}$ are arbitrary constants.

The solution of the given differential equation is $y = C_{1} e^{- x} + C_{2} e^{x} \cos x + C_{3} e^{x} \sin x$ , where $C_{1}, C_{2}, C_{3}$ are arbitrary constant.

Hence the final solution is $y (x) = c_{1} e^{- x} + c_{2} e^{- 5 x} + c_{3} e^{4 x}$

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

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

Step by Step Solution

Step 1: Auxiliary equation:

Step 2: Inspecting the sum further:

Step 3: General solution:

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Find a general solution for the differential equation with x as the independent variable: y'''−y''+2y=0

Step by Step Solution

Step 1: Auxiliary equation:

Step 2: Inspecting the sum further:

Step 3: General solution:

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

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