Find All the following Laplace Transformations once using the
definition of Laplace Transformation and then using the memorized
Laplace Table relationships:
L[sin(ω*t)]
L[(e-5t)cos(6t)]
L[(e-5t)(t2)]
3. Solve the following differential equations by using LaPlace
transformation:
2x'' + 7x' + 3x = 0; x(0) = 3, x'(0) = 0
x' + 2x = ?(t); x(0-) = 0
where ?(t) is a unit impulse input given in the LaPlace
transform table.