Explanation Given: The rate of decay is 40 e − 20 t kg / sec . The value of decay constant is 5 / sec . Procedure: The standard form of the equation is, d y d x + P ( x ) y = Q ( x ) Calculate the integrating factor. μ ( x ) = exp [ ∫ P ( x ) d x ] Multiply the standard form by μ ( x ) Integrate the obtained equation and solve for y by diving by μ ( x ) . Calculation: Consider the following equation. d y d t + rate of creation − rate of decay ⋯ ( 1 ) Substitute the values in above equation. d y d t + 40e − 20 t − k y ⋯ ( 2 ) Substitute 5 / sec for k in equation ( 2 ) . d y d t = 40e − 20 t − 5 y d y d t + 5 y − 40e − 20 t = 0 ⋯ ( 3 ) Calculate the integrating factor. μ ( t ) = e ( ∫ 5 d t ) = e 5 t Multiply equation ( 3 ) by e 5 t . e 5 t d y d t + ( 5 y ) e 5 t − e 5 t ( 40e − 20 t ) = 0 d d t ( e 5 t y ) = e 5 t ( 40e − 20 t ) Integrate the above equation

Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)

7th Edition

ISBN: 9780137394524

Author: R. Nagle, Edward Saff

Publisher: PEARSON+

See similar textbooks

Question

Chapter 2.3, Problem 23E

To determine

The mass y(t) of RA2 for t≥0 if initially y(0)=10 kg.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.3, Problem 22E

Chapter 2.3, Problem 24E

Students have asked these similar questions

A smallish urn contains 25 small plastic bunnies – 7 of which are pink and 18 of which are white. 10 bunnies are drawn from the urn at random with replacement, and X is the number of pink bunnies that are drawn. (a) P(X = 5) ≈ (b) P(X<6) ≈ The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a) The probability that the Grinch gets exactly 6 blue marbles is [ Select ] ["≈ 0.054", "≈ 0.043", "≈ 0.061"] . (b) The probability that the Grinch gets at least 7 blue marbles is [ Select ] ["≈ 0.922", "≈ 0.905", "≈ 0.893"] . (c) The probability that the Grinch gets between 8 and 12 blue marbles (inclusive) is [ Select ] ["≈ 0.801", "≈ 0.760", "≈ 0.786"] . The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a)…

Using Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates).

Consider the alphabet {a, b, c}.• Design a regular expression that recognizes all strings over {a, b, c} that have at least three nonconsec-utive c characters (two characters are non-consecutive if there is at least one character between them)and at least one a character.• Explain how your regular expression recognizes the string cbbcccac by clearly identifying which partsof the string match to the components of your regular expression

Chapter 2 Solutions

Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)

Ch. 2.2 - Prob. 1E Ch. 2.2 - In Problems 1-6, determine whether the given...Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E

Knowledge Booster

The mass y ( t ) of R A 2 for t ≥ 0 if initially y ( 0 ) = 10 kg .

The mass y(t) of RA2 for t≥0 if initially y(0)=10 kg.

Want to see the full answer?

Chapter 2 Solutions