Use the Laplace transform to solve the given initialvalue pr

Use the Laplace transform to solve the given initial-value problem.

y\'\' 6y\' + 13y = 0,  y(0) = 0,  y\'(0) = 9

Solution

Given:y\'\' 6y\' + 13y = 0,  y(0) = 0,  y\'(0) = 9

Taking the Laplace transform of both sides gives

           L{y\'\' 6y\' + 13y} = 0

           L{y\'\'}6L{y\'}+13L{y}=0

s^2L{y}-sy(0)-y\'(0)-y\'(0)-6(sly-y10))+13L{y}=0

(s^2-6s+13)L{Y}-9=0

L{y}=9/s^2-6s+13

y=L^-1[9/[s^2-6s+13]]    

no real values for s^2-6s+13.