Program Explanation Given information: The differential equation is x d y d x − y = 2 x 2 y and initial condition is y ( 1 ) = 1 . Concept used: The differential equation is 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 Calculation: The given differential equation is x d y d x − y = 2 x 2 y . Separate the variables of the above differential equation as, d y d x = 2 x 2 y + y x d y d x = ( 2 x 2 + 1 ) y x d y y = ( 2 x 2 + 1 ) x d x Now integrate the equation on both the sides as, ∫ d y y = ∫ ( 2 x 2 + 1 ) x d x ln y = 2 x 2 2 + ln x + C y = e x 2 + ln x + C y = e C x e x 2 Here, C is the constant of integration

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

Question

Chapter 1.4, Problem 25P

Program Plan Intro

To find: The particular solution of the initial value problem xdydx−y=2x2y and the initial condition is y(π2)=π2 .

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Chapter 1.4, Problem 24P

Chapter 1.4, Problem 26P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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The particular solution of the initial value problem x d y d x − y = 2 x 2 y and the initial condition is y ( π 2 ) = π 2 .

Solution Summary: The author explains how the differential equation is xdy -y = 2x & y=2y. Separate the variables and integrate the equation.

Concept explainers

To find: The particular solution of the initial value problem xdydx−y=2x2y and the initial condition is y(π2)=π2 .

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Chapter 1 Solutions