hw_3_5_6_09

hw_3_5_6_09 - MA 221 Homework Solutions Due date: March...

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MA 221 Homework Solutions Due date : March 5 / 6 , 2009 7 . 5p . 383 # 1 ̄ , 3 , 5 ̄ , 6 ̄ , 7 , 1 ̄ 5 ̄ , 17 , 1 ̄ 9 ̄ (Underlined problems are to be handed in) For problems 1, 3, 5, and 6, solve the given initial value problem using the method of Laplace transforms. 1 ̄ .) y ′′ 2 y 5 y 0; y 0 2, y 0 4 Taking the Laplace transform of y ′′ 2 y 5 y 0 and applying the linearity of the Laplace transform yields: L y ′′ 2 L y 5 L y L 0 If we put Y s L y  s and apply properties (2) and (4) on pages 361 and 362 of the text, we get: L y sY s y 0 sY s 2 and L y ′′ s 2 Y s sy 0 y 0 s 2 Y s 2 s 4 Substituting these expressions and using the fact that L 0 0 and solving for Y s yields s 2 Y s 2 s 4 2 sY s 2 5 Y s 0 Solving for Y s
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This note was uploaded on 09/22/2009 for the course MA MA221 taught by Professor Levine during the Spring '09 term at Stevens.

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hw_3_5_6_09 - MA 221 Homework Solutions Due date: March...

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