# EXAM2 - Problem 1(17pts Solve y 00 xy 2 y = 0 y(0 = 1 y(0 =...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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.

Unformatted text preview: Problem 1 (17pts) . Solve y 00 + xy + 2 y = 0 , y (0) = 1 , y (0) = 0 , by means of a power series about x = 0. Find the recurrence relation and compute the first three nonzero terms. Find the closed formula for the coefficients and compute the radius of convergence of the power series. 1 Problem 2 (10pts) . Consider the following 2nd order differential equation (2 x 2- x + 1) y 00 + ln(1 + x ) y + cos ( sin( x ) ) y = xe x 2 y (0) = y (0) = 1 . (1) Is the solution of equation (1) analytic around x = 0? If so, what is the optimal lower bound for the radius of convergence of the power series of y at 0 you can guarantee? Also, find the polynomial of degree 3 that best approximates y in a neighborhood of 0. 2 Problem 3 (6pts + 8pts + 8pts) . Consider the Euler equation x 2 y 00 + αxy + βy = 0 , x > . (2) and let F ( r ) = r ( r- 1) + αr + β . From item (a) to item (c), justify every single step of your solution. Show all the work....
View Full Document

{[ snackBarMessage ]}

### Page1 / 13

EXAM2 - Problem 1(17pts Solve y 00 xy 2 y = 0 y(0 = 1 y(0 =...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online