(a) Explanation Given information: A differential equation and its associated slope field are given and foreach equation is given as, d y d t = 2 y − t . Calculation: The given differential equation is, d y d t = 2 y − t To sketch the number of differential solutions on slope field calculation is as follows, Rewriting the equation, d y d t = 2 y − t d y d t − 2 y = − t T h i s i s t h e f i r s t o r d e r l i n e a r d i f f e r e n t i a l e q u a t i o n o f t h e t e r m , d y d t + p ( t ) y = g ( t ) H e r e , p ( t ) = − 2 a n d g ( t ) = − t T h e int e g r a t i n g f a c t o r i s , μ ( t ) = e ∫ p ( t ) d t = e − ∫ 2 d t = e − 2 t The solution of d y d t + p ( t ) y = g ( t ) i s , y = ∫ μ ( t ) g ( t ) d t + C μ ( t ) = (b) To determine To calculate: To describe briefly the behavior of the solution with y ( 0 ) = 1 2 a s t increases.

4th Edition

ISBN: 9780495561989

Author: Paul Blanchard, Robert L. Devaney, Glen R. Hall

Publisher: Cengage Learning

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Chapter 1.3, Problem 8E

(a)

To determine

To calculate: To sketch the number of differential solutions on the slope field.

(b)

To determine

To calculate: To describe briefly the behavior of the solution with y(0)=12 as t increases.

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Chapter 1.3, Problem 7E

Chapter 1.3, Problem 9E

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To sketch the number of differential solutions on the slope field.

Solution Summary: The author explains how to sketch the number of differential solutions on the slope field.