DEfall09HW11

DEfall09HW11 - MTH 2201/2202 Differential Equations/Linear...

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Unformatted text preview: MTH 2201/2202 Differential Equations/Linear Algebra F irst Order Systems of Dif f erential Equations 1. The given vectors are solutions of a system X = AX . Determine whether the vectors form a fundamental set on (−∞, ∞). 1 1 (i) X1 = e−2t , X2 = e−6t . 1 −1 1 3 2 1 1 (ii) X1 = −2 + t 2 , X2 = −2 , X3 = −6 + t 4 . 4 2 4 12 4 2. Find the general solution of the following systems dx = x+y−z dt −1 1 0 dy (ii) X = 1 2 1 X (i) = 2y dt 0 3 −1 dz = y−z dt dx = −x + 3y dt (iii) dy = −3x + 5y dt dx = 5x + y dt (v ) dy = −2x + 3y dt 3. Solve system the 1 −12 X = 1 2 11 5 −4 0 (iv ) X = 1 0 2 X 0 25 1 −1 2 (vi) X = −1 1 0 X −1 0 1 subject to the indicated initial condition −14 4 −3 X, X (0) = 6 . −2 −7 4. Solve the following nonhomogeneous systems. dx = 3x − 3y + 4 2 −1 dt (ii) X = (i) dy 42 = 2x − 2y − 1 dt X+ sin 2t 2 cos 2t e2t 1 (iii) X = 18 1 −1 X+ e−t tet 12 X + (iv ) X = 1 − 1 2 (iv ) X = 3 −1 −1 3 X+ csc t sec t 4e2t 4e4t et , X (0) = 1 1 2 ...
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This note was uploaded on 03/02/2011 for the course MATH 1101 taught by Professor Tenali during the Spring '11 term at FIT.

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DEfall09HW11 - MTH 2201/2202 Differential Equations/Linear...

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