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Rewrite the initial value problem in matrix form and verify that the given vector function is a solution. (a) y'_1 = y_1 + y_2 y_1 (0) = 1 y'_2 = -2y_1 + 4y_2, y_2 (0) = 0; y = 2 [1 1] e^2t - [1 2] e^3t (b) y'_1 = 5y_1 + 3y_2 y_1 (0) = 12 y'_2 = -y_1 + y_2, y_2 (0) = -6; y = 3 [1 -1] e^2t + 3[3 -1] e^4t Show transcribed image text Rewrite the initial value problem in matrix form and verify that the given vector function is a solution. (a) y'_1 = y_1 + y_2 y_1 (0) = 1 y'_2 = -2y_1 + 4y_2, y_2 (0) = 0; y = 2 [1 1] e^2t - [1 2] e^3t (b) y'_1 = 5y_1 + 3y_2 y_1 (0) = 12 y'_2 = -y_1 + y_2, y_2 (0) = -6; y = 3 [1 -1] e^2t + 3[3 -1] e^4t
![](https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/25/2530491.jpeg)
Rewrite the initial value problem in matrix form and verify that the given vector function is a solution. (a) y'_1 = y_1 + y_2 y_1 (0) = 1 y'_2 = -2y_1 + 4y_2, y_2 (0) = 0; y = 2 [1 1] e^2t - [1 2] e^3t (b) y'_1 = 5y_1 + 3y_2 y_1 (0) = 12 y'_2 = -y_1 + y_2, y_2 (0) = -6; y = 3 [1 -1] e^2t + 3[3 -1] e^4t
Show transcribed image text Rewrite the initial value problem in matrix form and verify that the given vector function is a solution. (a) y'_1 = y_1 + y_2 y_1 (0) = 1 y'_2 = -2y_1 + 4y_2, y_2 (0) = 0; y = 2 [1 1] e^2t - [1 2] e^3t (b) y'_1 = 5y_1 + 3y_2 y_1 (0) = 12 y'_2 = -y_1 + y_2, y_2 (0) = -6; y = 3 [1 -1] e^2t + 3[3 -1] e^4t1
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Lelia LubowitzLv2
31 Jan 2019