SOLUTION: Given that L{cos(7t)/sqrt(πt)}=e^(−7/s)/sqrt(s) find the Laplace transform of sqrt(t/π)cos(7t). L{sqrt(t/π)cos(7t)}= My answer (cos(3/2tan^(-1)(7/s)))/(2(s^2+49)^

Question 1185369: Given that
L{cos(7t)/sqrt(πt)}=e^(−7/s)/sqrt(s)
find the Laplace transform of sqrt(t/π)cos(7t).
L{sqrt(t/π)cos(7t)}=
My answer (cos(3/2tan^(-1)(7/s)))/(2(s^2+49)^(3/4)) , but is wrong
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
It is given that .

===> , by applying the definition of the Laplace transform to the hypothesis.

===> , i.e., taking derivatives wrt s.

===>

===>

Therefore,
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