undefined Solution To solve: The differential equation d y d x = e x + y y − 1 . The solution of the differential equation d y d x = e x + y y − 1 is − y e − y = e x + C _ . Formula used: u-v integration rule: ∫ u d v = u v − ∫ v d u Calculation: The differential equation is, d y d x = e x + y y − 1 Separate the variables and rewrite the differential equation as follows. d y d x = e x + y y − 1 d y d x = e x y − 1 y − 1 e y d y = e x d x ( y − 1 ) e − y d y = e x d x Integrate on both sides of the equation. ∫ ( y − 1 ) e − y d y = ∫ e x d x Integrate the above integral by the method of u-v substitution. Take u = y − 1 gives d u = d y and d v = e − y d y gives v = − e − y . Thus, the integral becomes, ∫ ( y − 1 ) ︸ u e − y d y ︸ d v = ∫ e x d x ( y − 1 ) ( − e − y ) − ∫ ( − e − y ) d y = e x + C − y e − y + e − y − e − y = e x + C − y e − y = e x + C Thus, the solution of the differential equation d y d x = e x + y y − 1 is − y e − y = e x + C _ .

Fundamentals of Differential Equations (9th Edition)

9th Edition

ISBN: 9780321977069

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

Publisher: PEARSON

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

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.6, Problem 48E

Chapter 2, Problem 2RP

Students have asked these similar questions

2. What constant interest rate is required if an initial deposit placed into an account that accrues interest compounded continuously is to double its value in five years? 3. Solve the equation (D³ + 3D² – 9D – 27)y = 0 4. Solve the equation (D4 + 13D² + 36)y = 0 5. Solve the equation (D* + 9D³ + 5D² – 93D – 90)y = 0

For each dif erential equation in Problems 1–21, find the general solutionby finding the homogeneous solution and a particular solution. Please DO NOT YOU THE PI method where 1/f(r) * x. Dont do that. Instead do this, assume for yp = to something, do the 1 and 2 derivative of it and then plug it in the equation to find the answer.

II. Solve xdy + (3x – 2y)dx = 0 in two ways. 1. First Method 2. Second Method

Chapter 2 Solutions

Fundamentals of Differential Equations (9th Edition)

Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 716, solve the equation. 7. xdydx=1y3 Ch. 2.2 - In Problems 716, solve the equation. 8. dxdt=3xt2 Ch. 2.2 - In Problems 716, solve the equation. 9....Ch. 2.2 - In Problems 716, solve the equation. 10....

Knowledge Booster

$Advanced Math$

Learn more about

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

In Problems 1–30 , solve the equation . 1. d y d x = e x + y y − 1

Concept explainers

Videos

Want to see more full solutions like this?

Want to see the full answer?

Chapter 2 Solutions