If x''+x'-6x=e^(-t), with x(0)=x'(0)=0, what is the value of X(s)?

Cem Hayes 2021-01-10 Answered

If x+x6x=et,  with  x(0)=x(0)=0, what is the value of X(s)?

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Expert Answer

Layton
Answered 2021-01-11 Author has 89 answers
Step 1
Given
x+x6x=et,  with  x(0)=x(0)=0
To find X(s)
Step 2
Laplace transformation
L{x}=s2X(s)sx(0)x(0)
L{x}=sX(s)x(0)
L{x}=X(s)
L{et}=1s+1
Step 3
Laplace transformation of given differential equation is
L{x+x6x}=L{et}
s2X(s)sx(0)x(0)+sX(s)x(0)6X(s)=1s+1
s2X(s)+sX(s)6X(s)=1s+1
X(s)[s2+s6]=1s+1
X(s)[(s+3)(s2)]=1s+1
X(s)=1(s2)(s+1)(s+3)
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