Assignment #2 Solutions

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

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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 ) = . Correct Answers: 13 260 6908 2 + 13*x + 130*x*x +1151.33333333333*x*x*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 = Correct Answers: 0.5*(x ** 9) + 9.5 * (x ** 7) 4. (1 pt) Find u from the differential equation and initial condition. du dt = e - 3 t - u , u ( 0 ) = 6 . u = Correct Answers: (1/1)*ln(403.762126826068 + ((1/-3)*2.71828182845905ˆ(-3*t))) 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 = Correct Answers:

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

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