(a) Explanation Given: The initial value problem is, y ′ = y 2 , y ( 1 ) = 1 The family of solutions is, y = − 1 x + c Substitute 1 for y and 1 for x in the given family of solutions. 1 = − 1 1 + c c + 1 = − 1 c = − 1 − 1 c = − 2 Substitute − 2 for c in given family of solutions (b) To determine To show: y = 1 2 − x is the solution from given family that satisfies the given initial value problem. (c) To determine Determine the solutions in part (a) and part (b) are same or not.

Bundle: Differential Equations with Boundary-Value Problems, Loose-leaf Version, 9th + WebAssign Printed Access Card for Zill's Differential Equations ... Problems, 9th Edition, Single-Term

9th Edition

ISBN: 9781337604901

Author: Dennis G. Zill

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 1.2, Problem 32E

(a)

To determine

To show: y=12−x is the solution from given family that satisfies the given initial value problem.

(b)

To determine

To show: y=12−x is the solution from given family that satisfies the given initial value problem.

(c)

To determine

Determine the solutions in part (a) and part (b) are same or not.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1.2, Problem 31E

Chapter 1.2, Problem 33E

Students have asked these similar questions

Theorem 1: A number n ∈ N is divisible by 3 if and only if when n is writtenin base 10 the sum of its digits is divisible by 3. As an example, 132 is divisible by 3 and 1 + 3 + 2 is divisible by 3.1. Prove Theorem 1 2. Using Theorem 1 construct an NFA over the alphabet Σ = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}which recognizes the language {w ∈ Σ^(∗)| w = 3k, k ∈ N}.

Recall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)

Find the sum of products expansion of the function F(x, y, z) = ¯x · y + x · z in two ways: (i) using a table; and (ii) using Boolean identities.

Chapter 1 Solutions

Bundle: Differential Equations with Boundary-Value Problems, Loose-leaf Version, 9th + WebAssign Printed Access Card for Zill's Differential Equations ... Problems, 9th Edition, Single-Term

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

y = 1 2 − x is the solution from given family that satisfies the given initial value problem.

Solution Summary: The author explains that y=12-x is the solution from given family that satisfies the given initial value problem.

Concept explainers

Videos

To show: y=12−x is the solution from given family that satisfies the given initial value problem.

To show: y=12−x is the solution from given family that satisfies the given initial value problem.

Determine the solutions in part (a) and part (b) are same or not.

Want to see the full answer?

Chapter 1 Solutions