![Calculus: Early Transcendentals, 2nd Edition](https://www.bartleby.com/isbn_cover_images/9780321965165/9780321965165_largeCoverImage.gif)
Cauchy-Euler equation with repeated roots One of several ways to find the second linearly independent solution of a Cauchy-Euler equation
a. What is the polynomial associated with this equation?
b. Show that if we let t = ex (or .x = ln t), then this equation becomes the constant coefficient equation
c. What is the characteristic polynomial for the equation in part (b)? Conclude that if the polynomial in part (a) has a repeated root, then the characteristic polynomial also has a repeated root.
d. Write the general solution of the equation in part (b) in the case of a repeated root.
e. Express the solution in part (d) in terms of the original variable t to show that the second linearly independent solution of the Cauchy-Euler equation is y = t(1–a)/2 ln t.
![Check Mark](/static/check-mark.png)
Trending nowThis is a popular solution!
![Blurred answer](/static/blurred-answer.jpg)
Chapter D2 Solutions
Calculus: Early Transcendentals, 2nd Edition
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)