ODE assignment6

# ODE assignment6 - Z 3 1 1 x dx 2 Use Euler Method with step...

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MAT 2384-Fall 2009-Homework #6 To be submitted in class on Friday, November 13 Question 1. In each case, find the solution to the linear homogeneous system of differential equa- tions: ~ y 0 = A~ y satisfying the given initial condition: ( i ) A = " 1 2 2 1 # , ~ y (0) = " 1 1 # ( ii ) A = " 3 - 5 1 - 1 # , ~ y (0) = " 1 0 # ( iii ) A = " 7 - 1 9 1 # , ~ y (0) = " 1 1 # ( iv ) A = " - 3 0 0 - 3 # , ~ y (0) = " - 1 0 # . Question 2. Solve the following nonhomogeneous systems: ( i ) ~ y 0 = " 1 3 3 - 1 # ~ y + " e x e 3 x # ( ii ) ~ y 0 = " 4 - 2 3 - 1 # ~ y + " - 2 x - 5 - 2 x - 3 # Question 3. 1. Use Gaussian Quadrature of order 4 to estimate the value of the integral
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Unformatted text preview: Z 3 1 1 + x dx. 2. Use Euler Method with step size h = 0 . 1 to approximate the values of the function y solution to the IVP: y = 3 x + 2 y, y (0) = 1 on the interval [0 , . 5]. Then solve the above diﬀerential equation and make a table to compare your approximations with the true values. 1...
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