Q4.3-17E Find a general solution y''-y'+7... [FREE SOLUTION]

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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: Q4.3-17E (page 172)

Find a general solution $y'' - y' + 7 y = 0$

Short Answer

Expert verified

The general solution of the given equation $y'' - y' + 7 y = 0$ isrole="math" localid="1654072330547" $y (t) = e^{\frac{}{}} ((c_{1} \cos (\frac{3 \sqrt{3}}{2} t) + c_{2} \sin (\frac{3 \sqrt{3}}{2} t))$

Step by step solution

Complex conjugate roots.

If the auxiliary equation has complex conjugate roots $伪卤 i 尾$ , then the general solution is given as: $y (t) = c_{1} e^{伪迟} 肠辞蝉尾迟 + c_{2} e^{伪迟} 蝉颈苍尾迟$ .

Finding the roots of the auxiliary equation.

Given differential equation is $y'' - y' + 7 y = 0 .$

Then the auxiliary equation is $r^{2} - r + 7 = 0 .$

The roots of the auxiliary equation are:

role="math" localid="1654072545156" $\begin{matrix} r = \frac{1 卤 \sqrt{1^{2} - 4 脳 1 脳 7}}{2 脳 1} \\ r = \frac{1 卤 \sqrt{1 - 28}}{2} \\ r = \frac{1 卤 \sqrt{- 27}}{2} \\ r = \frac{1 卤 3 \sqrt{3} i}{2} \end{matrix}$

Final answer.

Therefore, the general solution is:

$y (t) = e^{\frac{1}{2} t} (c_{1} \cos (\frac{3 \sqrt{3}}{2} t) + c_{2} \sin (\frac{3 \sqrt{3}}{2} t))$

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91影视

Find a general solution $y'' - y' + 7 y = 0$

Short Answer

Step by step solution

Complex conjugate roots.

Finding the roots of the auxiliary equation.

Final answer.

One App. One Place for Learning.

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91影视

Find a general solution y''-y'+7y=0

Short Answer

Step by step solution

Complex conjugate roots.

Finding the roots of the auxiliary equation.

Final answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Find a general solution $y'' - y' + 7 y = 0$