Program Explanation Given information: Differential equation is y ′ = 2 x y + 3 x 2 e x 2 and initial condition is y ( 0 ) = 5 . Formula used: If differential equation is, y ′ + p ( x ) y = q ( x ) Then integrating factor is, I . F . = e ∫ p ( x ) d x Then general solution of the differential equation is, y ( I . F . ) = ∫ q ( x ) ( I . F . ) d x + C Calculation: Consider, given differential equation as, y ′ = 2 x y + 3 x 2 e x 2 ....... (1) This equation can be rewritten as, y ′ − 2 x y = 3 x 2 e x 2 ....... (2) Now, integrating factor of the equation is, I . F

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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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 1.5, Problem 22P

Program Plan Intro

To find: The general solution of the differential equation y′=2xy+3x2ex2 . Also, find particular solution when initial condition is y(0)=5 .

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Chapter 1.5, Problem 21P

Chapter 1.5, Problem 23P

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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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The general solution of the differential equation y ′ = 2 x y + 3 x 2 e x 2 . Also, find particular solution when initial condition is y ( 0 ) = 5 .

Solution Summary: The author explains how to find the general solution of the differential equation yprime +2xy+3x2e

Concept explainers

To find: The general solution of the differential equation y′=2xy+3x2ex2 . Also, find particular solution when initial condition is y(0)=5 .

Want to see the full answer?

Chapter 1 Solutions