# dev52384 - Compute the true value of J to ﬁnd the error...

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MAT 2384A-Fall 2009-Homework #5 To be submitted in class on Tuesday, November 3 Question 1. For each of the following nonhomogeneous ODEs, Find the General Solution. If an initial condition is given, ﬁnd the corresponding unique solution. 1. x 3 y 000 - 3 x 2 y 00 + 4 xy 0 - 4 y = 1 x , x > 0 2. y 00 + y = 1 cos x 3. y 000 + y 00 - 2 y 0 = x 2 , y (0) = 1 , y 0 (0) = 2 , y 00 (0) = 0 4. y 00 - 2 y 0 + 2 y = e x + cos x, y (0) = 2 , y 0 (0) = - 1 5. x 2 y 00 + 3 xy 0 - 3 y = 1 x 2 , x > 0 , y (1) = 1 , y 0 (1) = 0 Question 2. Let J = Z 2 0 1 1 + x dx. 1. Use the Trapezoidal Rule to approximate the value of J within 0.01 of the true value.
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Unformatted text preview: Compute the true value of J to ﬁnd the error. Round your answers to 6 decimal places. 2. Use the Simpson’s Rule with n = 8 to approximate the value of J . Round your answers to 6 decimal places. Give bounds for your Error using the error bounds for Simpson’s Rule. Compare with the true value of the error using the true value for J . 1...
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