14th Edition

ISBN: 9780134507132

Author: Asmar

Publisher: YUZU

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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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Textbook Question

Chapter 5.1, Problem 14E

In Exercises 11 − 18 , solve the given differential equation with initial condition.

y ' = y , y ( 0 ) = 4 .

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Chapter 5.1, Problem 13E

Chapter 5.1, Problem 15E

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What is a solution to a differential equation? We said that a differential equation is an equation that describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential equation, we mean simply a function that satisfies this description. 2. Here is a differential equation which describes an unknown position function s(t): ds dt 318 4t+1, ds (a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate you really do get 4t +1. and check that dt' (b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation? (c) Is s(t)=2t2 + 3t also a solution to this differential equation? ds 1 dt (d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the right side of the equation by multiplying, and then integrate both sides. What do you get? (e) Does this differential equation have a unique solution, or an infinite family of solutions?

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In Exercises 11 − 18 , solve the given differential equation with initial condition. y ' = y , y ( 0 ) = 4 . .

Solution Summary: The author explains the unique solution of the differential equation y'=y with initial condition.

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