{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

389_pdfsam_math 54 differential equation solutions odd

# 389_pdfsam_math 54 differential equation solutions odd -...

This preview shows page 1. Sign up to view the full content.

Review Problems its degree, unless it’s the zero polynomial, we conclude that the linear combination (6.27) vanishes identically on ( −∞ , ) if and only if c 1 = c 2 = c 3 = c 4 = 0. This means that the given functions are linearly independent on ( −∞ , ). 5. (a) Solving the auxiliary equation yields ( r + 5) 2 ( r 2) 3 ( r 2 + 1) 2 = 0 ( r + 5) 2 = 0 or ( r 2) 3 = 0 or ( r 2 + 1) 2 = 0 . Thus, the roots of the auxiliary equation are r = 5 of multiplicity 2 , r = 2 of multiplicity 3 , r = ± i of multiplicity 2 . According to (22) on page 329 and (28) on page 330 of the text, the set of functions (assuming that x is the independent variable) e 5 x , xe 5 x , e 2 x , xe 2 x
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern