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Unformatted text preview: Stephanie Campbell Assignment 2 MATH263, Fall 2010 due 09/18/2010 at 11:55pm EDT. You may attempt any problem an unlimited number of times. 1. (1 pt) Suppose that the initial value problem y = 9 x 2 + 5 y 2- 7 , y ( ) = 2 has a solution in an interval about x = 0. Find y ( ) = . Find y 00 ( ) = . Find y 000 ( ) = . Note that for y 00 ( ) and y 000 ( ) you will have to differentiate the equation twice (remembering that y is a function of x ) and back substitute the values given or already calculated. The Taylor polynomial of degree 3 of the solution about x = is ( T 3 y )( x ) = . 2. (1 pt) Find the function y = y ( x ) (for x > 0 ) which satis- fies the differential equation x dy dx- 7 y = x 9 , ( x > ) with the initial condition: y ( 1 ) = 10 y = 3. (1 pt) Solve the initial value problem dy dx- 10tan ( 5 x ) y + 3sin ( 2 x ) = , y ( ) =- 4 . The solution is y ( x )= 4. (1 pt) Find u from the differential equation and initial condition....
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This note was uploaded on 12/01/2010 for the course MATH 263 taught by Professor Sidneytrudeau during the Fall '09 term at McGill.
- Fall '09