{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# m238sp06t3 - Mathematics 238 test three due Friday 1 Given...

This preview shows pages 1–2. Sign up to view the full content.

Mathematics 238 test three due Friday, May 26, 2006 1 . Given the initial value problem y + 169 y = 0 and y (0) = 0 and y (0) = 1 find the solution function y ( t ) determine the amplitude and the period of the solution y ( t ). find the first two positive values at which y ( t ) attains a local maximum value. 2 . Given the initial value problem y + 10 y + 169 y = 0 and y (0) = 0 and y (0) = 1 find the solution function y ( t ) determine the first two positive values at which y ( t ) attains a local maximum value calculate the quasi-period of the solution (the t -difference between locations of adjacent local maximum values) and the percentage decrease between adjacent maximum values. 3 . Use the variation of parameters technique to show that the solution to the initial value problem y + 4 y = g ( t ) and y (0) = 0 and y (0) = 0 is given by the formula y ( t ) = 1 2 t 0 - g ( s ) sin 2 s ds cos 2 t + 1 2 t 0 g ( s ) cos 2 s ds sin 2 t Show that this formula is equivalent to the more concise y ( t ) = 1 2 t 0 g ( s ) sin 2( t - s ) ds 4 . Given the differential equation ( x 2 + 9) y + 2 xy + 4 y

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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