2018328 1623 Lista+14 +Transformada+de+Laplace III

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Lista 14_Transformada de Laplace III 
 
Nos problemas de 1-18, (a)-(r) obtenha F(s) ou f(t), conforme indicado. 
(a) ℒ{𝑡𝑒10𝑡} 
(b) ℒ{𝑡𝑒−6𝑡} 
(c) ℒ{𝑡3𝑒−2𝑡} 
(d) ℒ{𝑡10𝑒−7𝑡} 
(e) ℒ{𝑡(𝑒𝑡 + 𝑒2𝑡)2} 
(f) ℒ{𝑒2𝑡(𝑡 − 1)2} 
(g) ℒ{𝑒𝑡𝑠𝑖𝑛 3𝑡} 
(h) ℒ{𝑒−2𝑡𝑐𝑜𝑠 4𝑡} 
(i) ℒ{(1 − 𝑒𝑡 + 3𝑒4𝑡)𝑐𝑜𝑠 5𝑡} 
(j) ℒ {𝑒3𝑡 (9 − 4𝑡 + 10𝑠𝑖𝑛 
𝑡
2
)} 
(k) ℒ−1 {
1
(𝑠+2)3
} 
(l) ℒ−1 {
1
(𝑠−1)4
} 
(m) ℒ−1 {
1
𝑠2−6𝑠+10
} 
(n) ℒ−1 {
1
𝑠2+2𝑠+5
} 
(o) ℒ−1 {
𝑠
𝑠2+4𝑠+5
} 
(p) ℒ−1 {
𝑠
𝑠2+6𝑠+34
} 
(q) ℒ−1 {
𝑠
(𝑠+1)2
} 
(r) ℒ−1 {
5𝑠
(𝑠−2)2
} 
2- Utilize a transformada de Laplace para resolver o problema de valor inicial dado. 
(a) 𝑦′ + 4𝑦 = 𝑒−4𝑡; 𝑦(0) = 2 
(b) 𝑦′ − 𝑦 = 1 + 𝑡𝑒𝑡; 𝑦(0) = 0 
(c) 𝑦′′ + 2𝑦′ + 𝑦 = 0 ; 𝑦(0) = 1, 𝑦′(0) = 1