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A first order linear differential equation is one that can be put in the form +P(z)y=Q(z) where P and Q are continuous functions on a given interval. This form is called the standard form and readily solved by multiplying both sides of the equation by an integrating factor, µ(z) = eS P(z) & In this problem, we want to find the general solution of the equation dy - y =-(2z" + 12x*) , z > 0 Part 1 We will begin by finding an integrating factor using the formula above, u(z) = es P(z) de µ(x) = Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by u(z) and re-write the left hand side as the derivative of a product giving us: P dz Part 3. Finally, upon integrating both sides with respect to z and solving for y we have:

A first order linear differential equation is one that can be put in the form +P(z)y=Q(z) where P and Q are continuous functions on a given interval. This form is called the standard form and readily solved by multiplying both sides of the equation by an integrating factor, µ(z) = eS P(z) & In this problem, we want to find the general solution of the equation dy - y =-(2z" + 12x*) , z > 0 Part 1 We will begin by finding an integrating factor using the formula above, u(z) = es P(z) de µ(x) = Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by u(z) and re-write the left hand side as the derivative of a product giving us: P dz Part 3. Finally, upon integrating both sides with respect to z and solving for y we have:

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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General Solution of a First Order Linear Differential Equation A first order linear differential equation is one that can be put in the form dy dr + P(z)y = Q(x) where Pand Q are continuous functions on a given interval. This form is called the standard form and is readily solved by multiplying both sides of the equation by an integrating factor, u(x) = el P(x) dz In this problem, we want to find the general solution of the equation fip - y = -(2x" + 12z“) , z > 0 Part 1. We will begin by finding an integrating factor using the formula above, u(z) = el P(z) dr µ(z) = Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by u(x) and re-write the left hand side as the derivative of a product giving us: d ( y dr Part 3. Finally, upon integrating both sides with respect to z and solving for y we have: y = NOTE: Type 'C' for the arbitrary constant in the general solution.
Transcribed Image Text:General Solution of a First Order Linear Differential Equation A first order linear differential equation is one that can be put in the form dy dr + P(z)y = Q(x) where Pand Q are continuous functions on a given interval. This form is called the standard form and is readily solved by multiplying both sides of the equation by an integrating factor, u(x) = el P(x) dz In this problem, we want to find the general solution of the equation fip - y = -(2x" + 12z“) , z > 0 Part 1. We will begin by finding an integrating factor using the formula above, u(z) = el P(z) dr µ(z) = Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by u(x) and re-write the left hand side as the derivative of a product giving us: d ( y dr Part 3. Finally, upon integrating both sides with respect to z and solving for y we have: y = NOTE: Type 'C' for the arbitrary constant in the general solution.
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