Inverse laplace of L^-1 {5s/s^2 + 3s - 4}

=  

Step-by-step explanation:

Step(i):-

Given

Factors of    s² + 3s - 4

               =    s² + 4s - s -4

               =   s( s +4 ) -1 (s +4)

               =   (s-1)(s+4)

              =    

By using partial fractions

            ..(i)

                s  = A ( s-1) + B( s+4) ....(ii)

          Put s= 1  in equation (ii) , we get

             1 = B(5)

         s = -4 in equation (ii) , we get

        -4 = -5A

Step(ii):-

    now the equation (i) , we get

By using inverse Laplace transform formula

                      =

x equals 1

step-by-step explanation:

f(4)=f(×)

x=1

your answer is -9

step-by-step explanation: