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DEfall09HW11

# DEfall09HW11 - MTH 2201/2202 Dierential Equations/Linear...

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MTH 2201/2202 Differential Equations/Linear Algebra First Order Systems of Differential Equations 1. The given vectors are solutions of a system X = AX . Determine whether the vectors form a fundamental set on ( -∞ , ). (i) X 1 = 1 1 e - 2 t , X 2 = 1 - 1 e - 6 t . (ii) X 1 = 1 - 2 4 + t 1 2 2 , X 2 = 1 - 2 4 , X 3 = 3 - 6 12 + t 2 4 4 . 2. Find the general solution of the following systems ( i ) dx dt = x + y - z dy dt = 2 y dz dt = y - z ( ii ) X = - 1 1 0 1 2 1 0 3 - 1 X ( iii ) dx dt = - x + 3 y dy dt = - 3 x + 5 y ( iv ) X = 5 - 4 0 1 0 2 0 2 5 X ( v ) dx dt = 5 x + y dy dt = - 2 x + 3 y ( vi ) X = 1 - 1 2 - 1 1 0 - 1 0 1 X 3. Solve the system subject to the indicated initial condition

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