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(2) Find the integrating factors of the differential equations below (link equations with product rule). Use the integrating factor and Fundamental Theorem of Calculus to solve the equation. If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with respect to z. (a) xy' + 3y = 2x5, y(2) = 1. (b) zy' = 3y+r¹ cos T, y(2T) = 0. (c) y' = 2xy + 3x² exp(r²), y(0) = 5.

(2) Find the integrating factors of the differential equations below (link equations with product rule). Use the integrating factor and Fundamental Theorem of Calculus to solve the equation. If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with respect to z. (a) xy' + 3y = 2x5, y(2) = 1. (b) zy' = 3y+r¹ cos T, y(2T) = 0. (c) y' = 2xy + 3x² exp(r²), y(0) = 5.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(2) Find the integrating factors of the differential equations below (link equations with product rule). Use the integrating factor and Fundamental Theorem of Calculus to solve the equation. If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with respect to a. (a) xy' + 3y = 2x³, y(2) = 1. (b) xy' = 3y + x² cos x, y(2n) = 0. (c) y' = 2xy + 3x² exp(x²), y(0) = 5.
Transcribed Image Text:(2) Find the integrating factors of the differential equations below (link equations with product rule). Use the integrating factor and Fundamental Theorem of Calculus to solve the equation. If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with respect to a. (a) xy' + 3y = 2x³, y(2) = 1. (b) xy' = 3y + x² cos x, y(2n) = 0. (c) y' = 2xy + 3x² exp(x²), y(0) = 5.
Expert Solution
Step 1

Concept:

The first order ordinary differential equation is 

dydx+p(x)y(x)=q(x)

The integrating factor is

I.F=e∫p(x)dx

The general solution of the first order ordinary differential equation is 

y(I.F)=∫(I.F)q(x)dx

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