Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 9: Q1E (page 442)

Solve the differential equation $f^{'} (t) 鈭� 5 f (t) = 0$ and find all real solutions of the differential equation.

Short Answer

Expert verified

The solution is $f (t) = C e^{5 t}$ .

Step by step solution

Definition of first order linear differential equation.

Consider the differential equation $f' (t) - a f (t) = g (t)$ where is a smooth function and $' a'$ is a constant. Then the general solution will be $f (t) = e^{a t} 鈭� e^{- a t} g (t) d t$ .

Determination of the solution

Consider the differential equation as follows.

$f' (t) - 5 f (t) = 0$

Now, the differential equation is in the form as follows.

$f' (t) - a f (t) = g (t)$ , where $g (t)$ is a smooth function, then the general solution will be as follows.

$f (t) = e^{a t} 鈭� e^{- a t} g (t) d t$

Compute the calculation of the solution.

Substitute the value $0$ for $g (t)$ and $5$ for $a$ in $f (t) = e^{a t} 鈭� e^{- a t} g (t) d t$ as follows.

$\begin{array}{l} f (t) = e^{a t} 鈭� e^{- a t} g (t) d t \\ f (t) = e^{5 t} 鈭� e^{- 5 t} 脳 0 脳 d t \\ f (t) = e^{5 t} 鈭� 0 脳 d t \\ f (t) = e^{5 t} 鈰� C \end{array}$

Hence, the solution for the linear differential equation $f' (t) - 5 f (t) = 0$ is $f (t) = C e^{5 t}$ .

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91影视

Solve the differential equation $f^{'} (t) 鈭� 5 f (t) = 0$ and find all real solutions of the differential equation.

Short Answer

Step by step solution

Definition of first order linear differential equation.

Determination of the solution

Compute the calculation of the solution.

One App. One Place for Learning.

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91影视

Solve the differential equationf'(t)鈭�5f(t)=0and find all real solutions of the differential equation.

Short Answer

Step by step solution

Definition of first order linear differential equation.

Determination of the solution

Compute the calculation of the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Decision Maths

Statistics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the differential equation $f^{'} (t) 鈭� 5 f (t) = 0$ and find all real solutions of the differential equation.