Program Explanation Given information: The differential equation is d y d x = 3 ( y + 7 ) x 2 . Explanation: The given differential equation can be solved by separable variable method and linear from method. The given differential equation can be written as, d y y + 7 = 3 x 2 d x The above equation is in separable form and it can be solved as, ∫ d y y + 7 = 3 ∫ x 2 d x ln ( y + 7 ) = 3 ⋅ x 3 3 + C ln ( y + 7 ) = x 3 + C y + 7 = e x 3 + C Simplify the above equation. y = D e x 3 − 7 Here, D is constant of integration and D = e C . The given differential equation can also be written as, d y d x = 3 x 2 y + 21 x 2 d y d x − 3 x 2 y = 21 x 2 The above equation is in form of linear first-order equation and its solution is calculated as, y e − 3 ∫ x 2 d x = 21 ∫ x 2 e − 3 ∫ x 2 d x y e − x 3 = 21 ∫ x 2 e − x 3 d x Consider the integral ∫ x 2 e − x 3 d x as I and evaluate

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

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

Publisher: PEARSON

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Chapter 1, Problem 31RP

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Program Description: Purpose of problem is to derive general solutions of the differential equation dydx=3(y+7)x2 in two different ways.

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Chapter 1, Problem 30RP

Chapter 1, Problem 32RP

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Chapter 1 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

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Program Description: Purpose of problem is to derive general solutions of the differential equation d y d x = 3 ( y + 7 ) x 2 in two different ways.

Solution Summary: The author explains that the given differential equation can be solved by separable variable method and linear from method.

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Program Description: Purpose of problem is to derive general solutions of the differential equation dydx=3(y+7)x2 in two different ways.

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Chapter 1 Solutions