Explanation Calculation: Consider the given equation. ( x + y − 1 ) d x + ( y − x − 5 ) d y = 0 … ( 1 ) The differential equations with linear coefficient have form, a 1 x + b 1 y + c 1 = 0 , a 2 x + b 2 y + c 2 = 0 Since b 1 = 1 is not equal to a 2 = − 1 and a 1 b 2 = ( 1 ) ( 1 ) is not equal to a 2 b 1 = ( − 1 ) ( 1 ) , let use the translation of axes. x = u + h Differentiate above equation. d x = d u Let y = v + k and differentiate. d y = d v Substitute d v for d y , d u for d x , u + h for x and v + k for y in equation ( 1 ) . ( u + h + v + k − 1 ) d u + ( v + k − u − h − 5 ) d v = 0 … ( 2 ) Here, h and k satisfy the equation. Now, h + k = 1 … ( 3 ) k − h = 5 … ( 4 ) Solve the equation ( 3 ) and equation ( 4 ) . k = 3 , h = − 2 So, x = u + ( − 2 ) x = u − 2 u = x + 2 And y = v + 3 v = y − 3 Substitute 3 for k and − 2 for h in equation ( 2 ) . ( u + 3 + v − 2 − 1 ) d u + ( v + 3 − u − 2 − 5 ) d v = 0 ( u + v ) d u + ( v − u ) d v = 0 ( u + v ) d u = − ( v − u ) d v d v d u = u + v u − v Simplify above equation to make it homogeneous. d v d u = 1 + v u 1 − v u … ( 5 ) Let v u = z and differentiate. v u = z v = z u d v d u = u d z d u + z Substitute u d z d u + z for d v d u in equation ( 5 )

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

See similar textbooks

Question

Chapter 2.6, Problem 29E

To determine

To solve:

The equation (x+y−1)dx+(y−x−5)dy=0, using equation with linear coefficient method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.6, Problem 28E

Chapter 2.6, Problem 30E

Students have asked these similar questions

Suppose we have a linear program in standard equation form maximize cx subject to Ax = b, x > 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that z = u+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.

Can the expert solve an Integral In detall? Hoxto³ W. 1 w = dw 大 90x103 80*10³ ⑥M = 1 1012 221 JW 70x10 80x103 © P= ± Sin (lw/+1) dw 70*10*A

Schoology → C Cportsk12.com bookmarks Sis Grades and Attendance Al Detector - the Original Al Che X GPTZero + portsmouth.schoology.com/common-assessment-delivery/start/7747152192?action=onresume&submissionId=1600790102 New Tab Home | Schoology Quadrilateral Quiz English If WXYZ is a square, and WY = 32, find XY. Round your answer to the nearest tenth. Z XY = R X Y POSSIBLE POINTS: 5 2 of 20 48 21 1 2 345678910 Next ▸ Δ ㄖㄨ All Bookmarks Schoology Help Center | PRIVACY POLICY | Terms of Use PowerSchool ©2025

Chapter 2 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

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 equation ( x + y − 1 ) d x + ( y − x − 5 ) d y = 0 , using equation with linear coefficient method.

To solve: The equation (x+y−1)dx+(y−x−5)dy=0, using equation with linear coefficient method.

Want to see the full answer?

Chapter 2 Solutions

To solve:

The equation (x+y−1)dx+(y−x−5)dy=0, using equation with linear coefficient method.