Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q22E

Expert-verified

Fundamentals Of Differential Equations And Boundary Value Problems

Found in: Page 332

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.

Register for Free I’ll do it later

Short Answer

Find a general solution for the given linear system using the elimination method of Section 5.2.
$\begin{array}{l} \frac{d^{2} x}{d t^{2}} - x + 5 y = 0 \\ 2 x + \frac{d^{2} y}{d t^{2}} + 2 y = 0 \end{array}$

_{$y (t) = c_{1} \cos (2 x) + c_{2} \sin (2 x)$ The solution is}

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Elimination method

In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Step 2: Solving linear system using the elimination method:

We will do the following question on the basis of solving linear system using the elimination method;

Most popular questions for Math Textbooks

Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decisions.

${e^{3 x}, e^{5 x}, e^{- x}}$ on $(- \infty, \infty)$

Find a general solution for the differential equation with x as the independent variable:

$2 y''' - y'' - 10 y' - 7 y = 0$

. use the annihilator method to determinethe form of a particular solution for the given equation.

$y'' - 6 y' + 9 y = s i n 2 x + x$

In Problems 38 and 39, use the elimination method of Section to find a general solution to the given system.

$d^{2} x / d t^{2} - x + y = 0 x + d^{2} y / d t^{2} - y = e^{3 t}$

find a differential operator that annihilates the given function

$x^{2} e^{x} - x s i n 4 x + x^{3}$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free