Explanation Given: The given differential equation is t 2 d y d t + y 2 = t y . Procedure used: Bernoulli’s differential equation: d y d x + P ( x ) y = f ( x ) y n Substitute the following. y 1 − n = u General differential equation: d y d x + P y = Q General solution equation: I u = ∫ I Q d t Here, the integrating factor is I . Calculation: Write the expression for Bernoulli’s differential equation. d y d x + P ( x ) y = f ( x ) y n (1) Substitute the following. y 1 − n = u Consider the given differential equation t 2 d y d t + y 2 = t y and write the equation in the form of Bernoulli’s differential equation. t 2 d y d t + y 2 = t y t 2 d y d t − t y = − y 2 d y d t − y t = − y 2 t 2 (2) Compare the equation (2) with the Bernoulli’s differential equation to obtain n as 2 . Substitute 2 for n in equation (1). y 1 − n = u y 1 − 2 = u y − 1 = u (3) Differentiate equation (3) with respect to t. y − 1 = u d y d t = d ( u − 1 ) d t d y d t = − u − 2 d u d t Substitute − u − 2 d u d t for d y d t and u -1 for y in equation (2)

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

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 2.5, Problem 19E

To determine

The solution of the given differential equation by using appropriate substitution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.5, Problem 18E

Chapter 2.5, Problem 20E

Students have asked these similar questions

Question Find the following limit. Select the correct answer below: ○ 0 ○ 3 ○ 6 ∞ 6x + 3e lim 00+2 x 2

What is the limit as x → ∞ of t(x) = = √81x2 -3x+5

show all steps

Chapter 2 Solutions

Differential Equations with Boundary-Value Problems (MindTap Course List)

Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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.

The solution of the given differential equation by using appropriate substitution.

Solution Summary: The author explains the solution of the given differential equation by using appropriate substitution.

Concept explainers

Videos

The solution of the given differential equation by using appropriate substitution.

Want to see the full answer?

Chapter 2 Solutions