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Unformatted text preview: Final Examination  Summer, 2007. Differential Equations/Linear Algebra MTH 2201 Time: 2 hours 07/06/2007 Max.Credit: 60 Answer all the questions. Make your answers precise and write legibly. Calculators are NOT allowed. 1. (a) Solve the following system of linear equations: a+b+c 5a + 4b + c + d 10a + 6b + +d 6a = = = = 0 0 2 1 [10] [5] (b) Find the inverse Laplace transform of the following function: Y (s) = 2s + 1 s(s + 1)(s2 + 4s + 6) (c) Use Laplace transform methods to solve the following initial value problem: y + 4y + 6y = 1 + et y(0) = 0, y (0) = 0 2. (a) Find a fundamental matrix (t) of the system of ODE x y = 3x  y = 9x  3y [5] [8] (b) Find the inverse 1 (t) of the fundamental matrix (t) obtained in part (a). [4] 1 (c) Find a particular solution (t) of x y using the formula (t) = (t) = 3x  y + 1 = 9x  3y + 3
t 0 [6] 1 (s)f (s) ds where f = 1 3 , and (t) is the fundamental matrix obtained in (a). (d) Find the general solution of the nonhomogeneous system in (c). [2] 3. (a) Transform the differential equation x2 y + xy + 4y = sin(2 ln x) into a differential equation with constant coefficients. [2] (b) Find the general solution of the differential equation with constant coefficients obtained in (a), using the method of undertemined coefficients. (c) Use the solution obtained in (b) to find the general solution of the differential equation in (a). 4. Compute A1 where 2 5 5 A = 1 1 0 . 2 4 3 5. Solve the differential equation (y 2 + ty)dt  t2 dy = 0. [5] [6] [2] [5] 2 ...
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This note was uploaded on 02/11/2012 for the course MTH 2201 taught by Professor Kigaradze during the Spring '08 term at FIT.
 Spring '08
 Kigaradze
 Differential Equations, Linear Algebra, Algebra, Equations

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