find the given inverse Laplace transform. L^{-1}\{\frac{s^2+1}{s(s-1)(s+1)(s-2)}\}

tricotasu

tricotasu

Answered question

2021-09-10

find the given inverse Laplace transform
L1{s2+1s(s1)(s+1)(s2)}

Answer & Explanation

gwibdaithq

gwibdaithq

Skilled2021-09-11Added 84 answers

L1{s2+1s(s1)(s+1)(s2)}
s2+1s(s1)(s+1)(s2)
partial fraction s
s2+1s(s1)(s+1)(s2)=As+Bs1+Cs+1+Ds2(1)
s2+1=A(s1)(s+1)(s2)+Bs(s+1)(s2)+Cs(s1)(s2)+Ds(s1)(s+1)(2)
Put s=0 in eqn (2)
1=A(1)(1)(2)+0+0+0
2A=1
A=12
Put s=1 in eqn (2)
1+1=A(0)+B(1)(1+1)(12)+C(0)+D(0)
2B=2
B=1
Put s=1 in eqn (2)
1+1=A(0)+B(0)+C(1)(11)(12)+D(0)
6C=2
C=13
Put s=2 in eqn (2)
4+1=A(0)+B(0)+C(0)+D(2)(21)(2+1)
5=D(2)(1)(3)
6D=5
D=56
Eqn (1)
s2+1s(s1)(s+1)(s2)=1s1s1s1131s+1+561s2
inverse laplace on both sides
 

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