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)^

Algebra ->  Inverses -> 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)^      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
It is given that L%28cos%287t%29%2Fsqrt%28pi%2At%29%29+=+e%5E%28-7%2Fs%29%2Fsqrt%28s%29.

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

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

===>

===>

Therefore,