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(a) Find the inverse Laplace Transform of 1 (s-3)(S-2)² (b) Use the Laplace Transform to solve the initial value problem y"-5y'+6y=2-U(t−2)e²(¹-2) y(0)=0, y'(0)=0 where U(t-2) is the Heaviside unit function defined by 0, if t≤2 U(t-2)= [1, if t>2

(a) Find the inverse Laplace Transform of 1 (s-3)(S-2)² (b) Use the Laplace Transform to solve the initial value problem y"-5y'+6y=2-U(t−2)e²(¹-2) y(0)=0, y'(0)=0 where U(t-2) is the Heaviside unit function defined by 0, if t≤2 U(t-2)= [1, if t>2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. f(t)= L-{F(s)} 1 t", n = positive integer ť, p>-1 sin at Table 1: Laplace Transforms cos at sinh at cosh at U(t-c)f(t-c) et f(t) f(") (t) F(s) = L {f(t)} 1 S 1 s-a n! s>0 " r(p+1) a s² + a²³ S s² + a² s> a s>0 . S> 0 S>0 S> 0 a s> 8²-q² + $> |a| S ²-² s> |a| e "F (s) F(s-c) SF (s)-s¹ f (0)-...-sf(-²) (0)-f("¹) (0)
Transcribed Image Text:1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. f(t)= L-{F(s)} 1 t", n = positive integer ť, p>-1 sin at Table 1: Laplace Transforms cos at sinh at cosh at U(t-c)f(t-c) et f(t) f(") (t) F(s) = L {f(t)} 1 S 1 s-a n! s>0 " r(p+1) a s² + a²³ S s² + a² s> a s>0 . S> 0 S>0 S> 0 a s> 8²-q² + $> |a| S ²-² s> |a| e "F (s) F(s-c) SF (s)-s¹ f (0)-...-sf(-²) (0)-f("¹) (0)
5. (a) Find the inverse Laplace Transform of 1 (s-3)(S-2)² (b) Use the Laplace Transform to solve the initial value problem y"-5y'+6y=2-U(t-2)e²(¹-2) y(0)=0, y'(0)=0 where U(t-2) is the Heaviside unit function defined by [0, if t≤2 U(t-2)=< 1, if t > 2 [You may use any results in Table 1].
Transcribed Image Text:5. (a) Find the inverse Laplace Transform of 1 (s-3)(S-2)² (b) Use the Laplace Transform to solve the initial value problem y"-5y'+6y=2-U(t-2)e²(¹-2) y(0)=0, y'(0)=0 where U(t-2) is the Heaviside unit function defined by [0, if t≤2 U(t-2)=< 1, if t > 2 [You may use any results in Table 1].
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