Program Explanation Given information: The differential equation is d y d x = 2 x y 2 + 3 x 2 y 2 and initial condition 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 d y d x = 2 x y 2 + 3 x 2 y 2 . Separate the variables of the above differential equation as, d y d x = y 2 ( 2 x + 3 x 2 ) d y y 2 = ( 2 x + 3 x 2 ) d x Now integrate the equation on both the sides as, ∫ d y y 2 = ∫ ( 2 x + 3 x 2 ) d x y − 2 + 1 − 2 + 1 = 2 x 2 2 + 3 x 3 3 + C − 1 y = x 2 + x 3 + C y = − 1 x 2 + x 3 + C Here, C is the constant of integration

5th Edition

ISBN: 8220100802454

Author: Calvis

Publisher: PEARSON

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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 1.4, Problem 26P

Program Plan Intro

To find: The particular solution of the initial value problem dydx=2xy2+3x2y2 and the initial condition is y(1)=−1 .

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Chapter 1.4, Problem 25P

Chapter 1.4, Problem 27P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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The particular solution of the initial value problem d y d x = 2 x y 2 + 3 x 2 y 2 and the initial condition is y ( 1 ) = − 1 .

Solution Summary: The author explains how the differential equation can be calculated with the help of separating the variables.

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To find: The particular solution of the initial value problem dydx=2xy2+3x2y2 and the initial condition is y(1)=−1 .

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Chapter 1 Solutions