# hw2 - t =-2 by the method of undetermined coeﬃcients 4...

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ASE 330M Linear System Analysis Unique Number: 12880, Spring 2007 Homework #2 Math Review Date given: February 6, 2007 Date Due: February 15, 2007 1. State whether the following ordinary diﬀerential equations are linear or nonlinear. You may assume t to be the independent variable and y ( t ) to be the dependent variable. Also determine the order of each of these diﬀerential equation systems: (i) ˙ y ( t ) + y ( t ) = 10 (ii) ¨ y ( t ) + ˙ y ( t ) y ( t ) = x ( t ) (iii) (1 - α y ( t ) + α ˙ y ( t ) = y 3 / 2 ( t ) for α = 1 (iv) ˙ y ( t ) x 2 ( t ) + 1 = y ( t ) + ¨ x ( t ) 2. Solve the following ﬁrst order ODEs: a) y ( t ) ˙ y ( t ) = sin 2 ωt , ω is a real constant. b) ˙ y ( t ) = y ( t )tanh t You may leave the integration constants within the solution. 3. Solve the ﬁrst order linear ODE ˙ y ( t ) - 2 y
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Unformatted text preview: ( t ) =-2 by the method of undetermined coeﬃcients. 4. Solve the following second linear ordinary diﬀerential equations: a) ¨ y ( t ) + ˙ y ( t )-2 y ( t ) = 0 subject to y (0) = 1 and y (1) = π . b) ¨ y ( t )-3 ˙ y ( t ) + 8 y ( t ) = 0 subject to y (0) =-1 and ˙ y (0) = 0. 5. Consider the following diﬀerential equation ¨ y ( t ) + 5 ˙ y ( t ) + 6 y ( t ) = ˙ x ( t ) + x ( t ) When the function x ( t ) = 6 t 2 is speciﬁed, use the method of undetermined coeﬃcients to ﬁnd the solution y ( t ) assuming initial conditions y (0) = 25 / 18, and ˙ y (0) =-2 / 3. 6. Matlab problems B.14, B.22, B.24, and B.39(a) from your textbook. 1...
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