Assignment #2

# Assignment #2 - Stephanie Campbell due at 11:55pm EDT...

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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 ( 0 ) = 2 has a solution in an interval about x = 0. Find y ( 0 ) = . Find y ( 0 ) = . Find y ( 0 ) = . Note that for y ( 0 ) and y ( 0 ) 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 = 0 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 > 0 ) 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 ) = 0 , y ( 0 ) = - 4 . The solution is y ( x ) = 4. (1 pt) Find u from the differential equation and initial condition. du dt = e - 3 t - u , u ( 0 ) = 6 . u = 5. (1 pt) Find the function y = y ( x ) (for x > 0 ) which satis- fies the differential equation dy dx = 9 + 16 x xy 2 , ( x > 0 ) with the initial condition: y ( 1 ) = 5 y = 6. (1 pt) Consider the differential equation y = 1 36 x ( 81 - y 2 ) This equation has the 2 constant solutions (in increasing or-

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• Winter '09
• SidneyTrudeau
• Math, Constant of integration, Boundary value problem

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