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 |

11th Edition

ISBN: 9781305713864

Author: HARSHBARGER

Publisher: CENGAGE L

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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

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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