Program Explanation Given information: The differential equation is d y d x = Cos 2 x and initial condition is y ( 0 ) = 1 . Concept used: The differential equation d y d x = f ( x ) g ( y ) can be calculated with the help of separating the variables as, ∫ d y g ( y ) = ∫ f ( x ) d x The integral of the function cos x is sin x . Calculation: The given differential equation is d y d x = Cos 2 x . Separate the variables of the above differential equation as, d y = Cos 2 x d x Now take t for 2 x and then differentiate with respect to x as, t = 2 x d t d x = 2 d x = d t 2 Now integrate the equation on both the sides. ∫ d y = ∫ Cos 2 x d x ........ (1) Now substitute t for 2 x and d x for d t 2 in equation (1)

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

Question

Chapter 1.2, Problem 8P

Program Plan Intro

To find: A particular function y=f(x) that satisfy the differential equation dydx=Cos2x and the initial condition is y(0)=1 .

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Chapter 1.2, Problem 7P

Chapter 1.2, Problem 9P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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A particular function y = f ( x ) that satisfy the differential equation d y d x = Cos 2 x and the initial condition is y ( 0 ) = 1 .

Solution Summary: The author explains how the differential equation dx=mathrmCos2x can be calculated by separating the variables.

Concept explainers

To find: A particular function y=f(x) that satisfy the differential equation dydx=Cos2x and the initial condition is y(0)=1 .

Want to see the full answer?

Chapter 1 Solutions