Find the Laplace transform if L\left\{f"(t)\right\}=\arctan\left(\frac{1}{s}\right)

Armorikam 2021-09-10 Answered

Find the Laplace transform if L{f"(t)}=arctan(1s),f(0)=2 and f(0)=1, find L{f(t)}

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Expert Answer

odgovoreh
Answered 2021-09-11 Author has 107 answers

Step 1
Formula used:
L{f"(t)}=s2L{f(t)}sf(0)f(0)
Given: L{f(t)}=arctan(1s)
f(0)=2,f(0)=1
To find: L{f(t)}
Step 2
Consider
L{f"(t)}=s2L{f(t)}sf(0)f(0)
Substitute all the values we get
arctan(1s)=s2L{f(t)}2s1
s2L{f(t)}=arctan(1s)+2s+1
L{f(t)}=arctan(1s)+2s+1s2
L{f(t)}=1s2arctan(1s)+2s+1s2
Step 3
ANSWER:
L{f(t)}=1s2arctan(1s)+2s+1s2

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