yy4y f0 1 f0 0 SolutionGiven expression y y 4y When we ta

Solution

Given expression,

y\'\' - y\' - 4y

When we take the Laplace Transform, we replace the expressions i the way shown below :

y\'\' => s² Y(s) - sf(0) - f \' (0)

y\' => s Y(s) - f(0)

y => Y(s)

L[ y\'\' - y\' - 4y ]

= [ s² Y(s) - sf(0) - f \' (0) ] - [ s Y(s) - f(0) ] - 4Y(s)

= [ s² Y(s) - s ] - [ s Y(s) - 1 ] - 4Y(s)

= (s² - s - 4) Y(s) - s + 1