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Fundamentals Of Differential Equations And Boundary Value Problems

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

$Math Studyset Vaia Explanations$ Math

9th Edition · 616 pages

ISBN: 9780321977069

Chapter 6: Q13E (page 337)

find a differential operator that annihilates the given function.
$e^{- 7 x}$

Short Answer

Expert verified

$D + 7$ is the differential operator that annihilates the given function.

Step by step solution

01

Differentiate the function continuously

Let the function be $f (x) = e^{- 7 x}$

Then

$f' (x) = - 7 e^{- 7 x} = - 7 f (x) \Rightarrow f' (x) + 7 f (x) = 0$

Hence $(D + 7) [f] = 0$

Then $D + 7$ is the differential operator that annihilates the given function.

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Most popular questions from this chapter

In Problems 1-6, use the method of variation of parameters to determine a particular solution to the given equation.

$y^{'''} - 3 y^{''} + 4 y = e^{2 x}$

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

${sinx, cosx, tanx}$ on $(- \frac{π}{2}, \frac{π}{2})$

Determine whether the given functions are linearly dependent or linearly independent on the interval $(0, \infty)$ .

(a) ${e^{2 x}, x^{2} e^{2 x}, e^{- x}}$

(b) ${e^{x} s i n 2 x, x e^{x} s i n 2 x, e^{x}, x e^{x}}$

(c) ${2 e^{2 x} - e^{x}, e^{2 x} + 1, e^{2 x} - 3, e^{x} + 1}$

In Problems 1-6, use the method of variation of parameters to determine a particular solution to the given equation.

$y^{'''} - 3 y^{''} + 3 y^{'} - y = e^{x}$

. find a differential operator that annihilates the given function.

$x^{4} - x^{2} + 11$

See all solutions

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