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s11_mthsc208_hw10

# s11_mthsc208_hw10 - MthSc 208 Spring 2011(Differential...

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MthSc 208, Spring 2011 (Differential Equations) Dr. Macauley HW 10 Due Thursday March 3rd, 2011 (1) Solve the following differential equations. (a) y 0 = - 3 y (b) 2 y 0 = t + 6 y (c) 2 y 0 = t 2 + 6 y (d) y 00 + 4 y = 0 (e) y 00 = - 9 y + 12. (2) For each system below, write it as Ax = b . Find all solutions, and sketch the graph of the lines in each system on the same axis. Are the resulting lines intersecting, parallel, or coincident? (a) x 1 + 3 x 2 = 0 , 2 x 1 - x 2 = 0 (b) - x 1 + 2 x 2 = 4 , 2 x 1 - 4 x 2 = - 6 (c) 2 x 1 - 3 x 2 = 4 , x 1 + 2 x 2 = - 5 (d) 3 x 1 - 2 x 2 = 0 , - 6 x 1 + 4 x 2 = 0 (e) 2 x 1 - 3 x 2 = 6 , - 4 x 1 + 6 x 2 = - 12 (3) For each part, find the determinant, eigenvalues and eigenvectors of the given matrix. If the matrix is invertible, find its inverse. (a) A = 3 - 2 2 - 2 (b) A = 3 - 2 4 - 1 (c)
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