HW6 Solutions.pdf - ESE 351-01 Fall 2017 Homework Set#6 due Oct 10 Use Unilateral ransform methods for all differential and difference equations No

# HW6 Solutions.pdf - ESE 351-01 Fall 2017 Homework Set#6 due...

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ESE 351-01, Fall 2017 Homework Set #6, due Oct. 10 Use Unilateral ransform methods for all differential and difference equations. No sketches. 6.1. Mukai 6.16.13(a) 6.2. Mukai 6.16.13(b) 6.3. Mukai 6.16.14(a) 6.4. Mukai 6.16.14(b) 6.5. Mukai 6.16.15(a) 6.6. Mukai 6.16.16(a) 6.7. Mukai 6.16.16(b) 6.8. Mukai 6.16.21(b) 6.9. Mukai 6.16.22(b) 6.10. Mukai 4.9.11, but using transform method. (Hint: long division.) 6.11. Mukai 5.6.6(b), (g) and (i), but use transform method. No sketches. 6.12. Mukai 6.16.26(b) 6.13. Mukai 6.17.1

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ESE 351-01, Fall 2017 Homework Set #6, due Oct. 10 Solutions 6.1 Mukai 6.16.13(a) !! y + 5 ! y + 6 y = 0 y 0 ( ) = 1 ! y 0 ( ) = 0 s 2 Y s + 5 sY 1 ( ) + 6 Y = 0 s 2 + 5 s + 6 ( ) Y = s + 5 Y s ( ) = s + 5 s + 2 ( ) s + 3 ( ) = 3 s + 2 2 s + 3 y t ( ) = 3 e 2 t 2 e 3 t ( ) 1 t ( ) 6.2. Mukai 6.16.13(b) !! y + 6 ! y + 9 y = 0 y 0 ( ) = 1 ! y 0 ( ) = 0 s 2 Y s + 6 sY 1 ( ) + 9 Y = 0 s 2 + 6 s + 9 ( ) Y = s + 6 Y s ( ) = s + 6 s + 3 ( ) 2 = 1 s + 3 + 3 s + 3 ( ) 2 y t ( ) = e 3 t + 3 te 3 t ( ) 1 t ( ) 6.3. Mukai 6.16.14(a) 12 y k ( ) + 7 y k 1 ( ) + y k 2 ( ) = 0 y 0 ( ) = 0 y 1 ( ) = 1 or 12 y k + 2 ( ) + 7 y k + 1 ( ) + y k ( ) = 0 12 z 2 Y z ( ) + 7 zY ( ) + Y = 0 12 z 2 + 7 z + 1 ( ) Y = 12 z Y z ( ) z = 12 3 z + 1 ( ) 4 z + 1 ( ) = 1 z + 1 3 ( ) z + 1 4 ( ) = A z + 1 3 + B z + 1 4 A = 1 1 3 + 1 4 = 1 1 12 = 12 B = 1 1 4 + 1 3 = 1 1 12 = 12 Y z ( ) = 12 z z + 1 3 + 12 z z + 1 4 y k ( ) = 12 1 3 ( ) k + 12 1 4 ( ) k 1 k ( ) = 12 1 4 ( ) k − − 1 3 ( ) k 1 k ( )