(a) Explanation Given information: In the current universe, acceleration due to gravity is constant, so that position follows a differential equation, d 2 p d t 2 = − g and when the gravity changes over time is given as, d 2 p d t 2 = − g t n . Calculation: The accelaration due to gravity is constant in the universe. Hence, the position follows the differential equation as shown below as, d 2 p d t 2 = − g ----- (1) Where, g = 10 m / s (b) To determine To find: The solution of the modified differential equation for different values of n

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

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 2.7, Problem 45E

(a)

To determine

To find:The solution of the normal differential equation.

(b)

To determine

To find:The solution of the modified differential equation for different values of n

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Chapter 2.7, Problem 44E

Chapter 2.7, Problem 46E

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Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

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The solution of the normal differential equation.

Solution Summary: The author explains how the accelaration due to gravity is constant in the universe, so the position follows a differential equation.