ep 2 We have found that the roots of the auxiliary equation are m₁ = -1 and m₂ = -2. In the case that the auxiliary equation for a second-order linear equation has two distinct, real roots, we know the complementary function is of the form yce+ce. Therefore, the complementary function is as follows. Yc-c₂e-x+c₂e-2x Let y₂e and y₂-e-2x be the two independent solutions which are terms of the complementary function. We will find functions u₂(x) and u₂(x) such that y-U₁₁+ ₂₂ is a particular solution. These new functions are found by calculating multiple Wronskians. First, find the following Wronskian. w(x₂(x), ₂(x)) - w(ex, e-2) x₂(x) x₂(x) 6-2x
ep 2 We have found that the roots of the auxiliary equation are m₁ = -1 and m₂ = -2. In the case that the auxiliary equation for a second-order linear equation has two distinct, real roots, we know the complementary function is of the form yce+ce. Therefore, the complementary function is as follows. Yc-c₂e-x+c₂e-2x Let y₂e and y₂-e-2x be the two independent solutions which are terms of the complementary function. We will find functions u₂(x) and u₂(x) such that y-U₁₁+ ₂₂ is a particular solution. These new functions are found by calculating multiple Wronskians. First, find the following Wronskian. w(x₂(x), ₂(x)) - w(ex, e-2) x₂(x) x₂(x) 6-2x
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage