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# HW6_2384f10 - Question 5 Consider the IVP y = 3 x 2 y y(0 =...

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MAT 2384A-Fall 2010-Homework #6 To be submitted in class on Friday, December 3 Question 1. Find the Laplace Transform of the following fonctions: (1) sinh(2 t ) + 2 e - 2 t (2) - 2 t 3 + 5 t 2 + 6 (3) 2 cos( - 2 t ) + 3 sin( - 2 t ) (4) e - 3 t cos(2 t ) (5) u ( t - π ) sin(2 t ) Question 2. Find the Inverse Laplace Transform of the following fonctions: (1) 2 s - 5 s 2 - 3 s +2 (2) 3 s +2 s 2 +9 (3) e - 2 s s s 2 +9 Question 3. Use the Laplace Transform to solve the following initial value problems: (1) y 00 + 6 y 0 - 7 y = 0 , y (0) = - 2 , y 0 (0) = 3 (2) y 00 + 3 y 0 + 2 y = 2 e - 3 t , y (0) = 5 , y 0 (0) = 4 (3) y 00 + y = ( 0 , 0 < t < 3 - 2 t, t 3 , y (0) = 0 , y 0 (0) = 2 Question 4. Use Gaussian Quadrature of order 4 to estimate the value of the integral Z 1 0 x 1 + x dx. Round your numbers (nodes and coefficients) to 6 decimal places. Compute the exact value of the
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Unformatted text preview: Question 5. Consider the IVP: y = 3 x + 2 y, y (0) = 1 . (1) Use Euler Method with step size h = 0 . 1 to approximate the values of the function y solution to the IVP on the interval [0 , . 4]. (2) Use the Improved Euler Method with step size h = 0 . 1 to approximate the values of the function y solution to the IVP on the interval [0 , . 4]. (3) Solve the IVP to ﬁnd the exact solution. Make a table to compare your approximations found in parts (1) and (2) with the exact values. 1...
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