Explanation The given equation is d 2 y d x 2 − d y d x − 30 y = 10 which is equivalent to D 2 y − D y − 30 y = 10 . Note that the solution of the auxiliary equation m 2 − m − 2 = 0 gives the roots m 1 = − 5 and m 2 = 6 . Thus, y c = c 1 e − 5 x + c 2 e 6 x . Note that the proper form of y p is y p = A . This means that D y p = 0 and D 2 y p = 0 . Substitute y p and its derivatives into the differential equation as follows

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Chapter 31.9, Problem 17E

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To solve: The differential equation d2ydx2−dydx−30y=10.

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Chapter 31.9, Problem 16E

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Chapter 31 Solutions

Basic Technical Mathematics

Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

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The differential equation d 2 y d x 2 − d y d x − 30 y = 10 .

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