To determine To solve: The differential equation ( 1 + x ) y ′ + y = x . Explanation Procedure used: To solve the linear equation y ′ + P ( x ) y = Q ( x ) , multiply both sides by the integrating factor v ( x ) = e ∫ P ( x ) d x and integrate on both sides. The equation can also be solved directly by using the formula y = 1 v ( x ) ∫ v ( x ) Q ( x ) d x . Calculation: Rewrite the differential equation ( 1 + x ) y ′ + y = x in the standard form as follows. ( 1 + x ) y ′ + y = x d y d x + 1 1 + x y = x 1 + x Compare the above equation with the standard form d y d x + P ( x ) y = Q ( x ) . Here, P ( x ) = 1 1 + x and Q ( x ) = x 1 + x . Evaluate the value of ∫ P ( x ) d x as follows. ∫ P ( x ) d x = ∫ 1 1 + x d x = ln ( 1 + x ) Evaluate the integrating factor as follows

Thomas' Calculus - MyMathLab Integrated Review

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ISBN: 9780134786223

Author: Hass

Publisher: PEARSON

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Chapter 9.2, Problem 6E

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To solve: The differential equation (1+x)y′+y=x.

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Chapter 9.2, Problem 5E

Chapter 9.2, Problem 7E

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Chapter 9 Solutions

Thomas' Calculus - MyMathLab Integrated Review

Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - In Exercises 7–12, write an equivalent first-order...Ch. 9.1 - Prob. 10E

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