Explanation Given Information: The provided differential equation is d y = ( x 2 − 1 x + 1 ) d x and the value is y ( 0 ) = 1 3 . Formula used: Solution of the differential equation d y = f ( x ) d x is y = ∫ f ( x ) d x . The logarithmic formula of integration is ∫ 1 x + a d x = ln | x + a | + C , where a is any real number. The power of x formula of integration is ∫ x n d x = x n + 1 n + 1 + C , where n ≠ − 1 . Calculation: Consider the differential equation, d y = ( x 2 − 1 x + 1 ) d x Integrate both sides of the equation, ∫ d y = ∫ ( x 2 − 1 x + 1 ) d x y = x 2 + 1 2 + 1 − ln | x + 1 |

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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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…

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Chapter 12.5, Problem 14E

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To calculate: The particular solution to the differential equation dy=(x2−1x+1)dx if y(0)=13.

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Chapter 12.5, Problem 13E

Chapter 12.5, Problem 15E

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Chapter 12 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 12.1 - 1. True or false: (a) (b) Ch. 12.1 - Prob. 2CP Ch. 12.1 - 1. If what is Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

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The particular solution to the differential equation d y = ( x 2 − 1 x + 1 ) d x if y ( 0 ) = 1 3 .

Solution Summary: The author calculates the differential equation dy=(x2-1x+1)dx and the logarithmic formula of integration.

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To calculate: The particular solution to the differential equation dy=(x2−1x+1)dx if y(0)=13.

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Chapter 12 Solutions