Systems - MAT 2384-Practice Problems on Systems of Differential Equations In each case solve the Systems of Differential Equations Y = AY F(x for

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Unformatted text preview: MAT 2384-Practice Problems on Systems of Differential Equations In each case, solve the Systems of Differential Equations Y = AY + F (x) for the given matrix A and the vector F (x). If an initial condition is given, solve the corresponding IVP. 1. A = 1 0 0 −1 −1 −1 4 1 3 7 5 1 0 −4 1 1 4 2 −2 −1 4 1 1 3 1 0 0 −1 1 0 1 −1 −1 2 1 −3 4 2 1 0 , F ( x) = 2 ex 3e−2x 4e−x e−2x 2ex 3x 3 x2 + 2 x + 1 x+2 −3 sin(3x) 9 cos(3x) − 16 sin(3x) −5x2 + 6x + −x + 2x + −5 sin x 17 cos x −x2 + 6x −x + x − 1 x −x 0 ex 2 2 4 3 1 3 2. A = , F ( x) = , Y (0) = 5 7 −5 4 3. A = , F (x) = 4. A = , F ( x) = 5. A = , F (x) = 6. A = , F (x) = , Y (0) = 5 2 2 0 0 7. A = , F ( x) = , Y (0) = 8. A = , F (x) = , Y (0) = −1 9. A = , F (x) = 10. A = , F (x) = 1 ...
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This note was uploaded on 02/02/2011 for the course MATH MAT 2384 taught by Professor Khoury during the Spring '10 term at University of Ottawa.

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