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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 + P(z)y= Q(z) dr 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(z) = eS P(z) dz_ In this problem, we want to find the general solution of the equation dy y = -(2x7 + 12z4) , x >0 dr Part 1. We will begin by finding an integrating factor using the formula above, µ(x) = eS P(z) dz H(z) Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by µ(2) and re-write the left hand side as the derivative of a product giving us: dz Part 3. Finally, upon integrating both sides with respect to z and solving for y we have: NOTE: Type 'C'for the arbitrary constant in the general solution.

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 + P(z)y= Q(z) dr 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(z) = eS P(z) dz_ In this problem, we want to find the general solution of the equation dy y = -(2x7 + 12z4) , x >0 dr Part 1. We will begin by finding an integrating factor using the formula above, µ(x) = eS P(z) dz H(z) Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by µ(2) and re-write the left hand side as the derivative of a product giving us: dz Part 3. Finally, upon integrating both sides with respect to z and solving for y we have: NOTE: Type 'C'for the arbitrary constant in the general solution.

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 + P(z)y= Q(z) dr 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(z) = eS P(z) dz_ In this problem, we want to find the general solution of the equation dy y = -(2x7 + 12z4) , x >0 dr Part 1. We will begin by finding an integrating factor using the formula above, µ(x) = eS P(z) dz H(z) Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by µ(2) and re-write the left hand side as the derivative of a product giving us: dz Part 3. Finally, upon integrating both sides with respect to z and solving for y we have: 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 + P(z)y= Q(z) dr 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(z) = eS P(z) dz_ In this problem, we want to find the general solution of the equation dy y = -(2x7 + 12z4) , x >0 dr Part 1. We will begin by finding an integrating factor using the formula above, µ(x) = eS P(z) dz H(z) Hint: you should first re-write the equation in standard form. Part 2. Next, we multiply both sides of the differential equation by µ(2) and re-write the left hand side as the derivative of a product giving us: dz Part 3. Finally, upon integrating both sides with respect to z and solving for y we have: NOTE: Type 'C'for the arbitrary constant in the general solution.
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