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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 4: Q4.3-12E (page 172)

Find a general solution $u'' + 7 u = 0$

Short Answer

Expert verified

The general solution of the given equation $u'' + 7 u = 0$ is:

$y (t) = (c_{1} \cos (\sqrt{7} t) + c_{2} \sin (\sqrt{7} t))$ .

Step by step solution

01

Differentiate the value of u.

Given differential equation is $u'' + 7 u = 0$

02

Finding roots of the auxiliary equation.

The auxiliary equation is $r^{2} + 7 e = 0 .$

role="math" localid="1654069093148" $\begin{matrix} r^{2} + 7 = 0 \\ r^{2} = - 7 \\ r = 卤 \sqrt{7} i \end{matrix}$

03

Final answer.

Therefore, the general solution is:

$y (t) = e^{0 脳 t} (c_{1} \cos (\sqrt{7} t) + c_{2} \sin (\sqrt{7} t)) y (t) = (c_{1} \cos (\sqrt{7} t) + c_{2} \sin (\sqrt{7} t))$

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Most popular questions from this chapter

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation. $ty'' - y' + 2 y = \sin 3 t$

Determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) $y'' + 2 y' + 2 y = 8 t^{3} e^{- t} sint$

Find a general solution $z " + 10 z' + 25 z = 0$

Find a particular solution to the differential equation.

$y'' - 2 y' + y = 8 e^{t}$

Find a particular solution to the differential equation.

$2 z'' + z = 9 e^{2 t}$

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