Homework SourseSolve the following initial value problem using Laplace tran
Solve the following initial value problem using Laplace transforms. Usestep(t-c)for![\"\\mathcal{U}(t-c)\"](\"//webwork.wallawalla.edu/webwork2_files/tmp/equations/33/fedd6872c3ed679d0b54f19320ae431.png\") .![\"y\'\'](\"//webwork.wallawalla.edu/webwork2_files/tmp/equations/a2/21f798793ac607163deeddd3964e411.png\") ![\"y(t)=\"](\"//webwork.wallawalla.edu/webwork2_files/tmp/equations/93/17bd0d42027f77677147cf4e2d37c91.png\") |
Solution
s2 Y(s)-sy(0)-y\'(0)-6sY(s)+6y(0)-7Y(s)=e-5s
s2 Y(s)-6sY(s)-7Y(s)=e-5s
Y(s)[s2 -6s-7]=e-5s
Y(s)=e^(-5s)/[s2 -6s-7]
Y(s)= e^(-5s)/[(s-7)(s-1)]
Y(s)=e^(-5s)[1/(s-7) +1/(s-1)]/6
taking laplace inverse
y(t) = [(e^7t +e^t)/6]* (t-5)
