MAT 275 Practice Final Exam B Key(1).pdf - MAT 275 Practice...

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MAT 275: Practice Final Exam B - Key Author: Blake Marx Solving IVP’s with Discontinuous Forcing Functions: 1. Find the y ( t ) that satisfies y 00 + 2 y 0 + y = f ( t ) = 0 (0) = - 4 . Write f ( t ) = sin( t ) u 2 π ( t ). ( 0 0 t < 2 π sin( t ) t 2 π , y (0) = 2 , y Impulse Functions: 1. Find the y ( t ) that satisfies y 00 + 5 y 0 + 6 y = 7 δ ( t - 4), y (0) = 0 , y 0 (0) = 1 . Intoduction to Systems of ODE’s: 1. Convert y 000 + 10 y 00 + 25 y 0 = sin( t ) + t into a system of ODE’s. Express the system in matrix form.
Matrices, Basic Theory of Systems: 1. Consider the system x 0 = 3 - 4 0 1 x. Verify that x 1 = 1 0 e 3 t is a solution and find a second linearly independent solution.

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