Hi all. I have been trying to relearn the laplace transform. I want to solve this second order ode
I know this can be easier done using the characteristic equation but I want to use the laplace tansform for learning purposes
here is my solution - is this right? have i done something stupid?
step 1 -
*here i am confused. With no initial conditions does the equation become*
step 2 - I factorise the quadratic and that becomes
*i am sure what i did here with partial fractions is wrong*
step 3 - take the inverse laplace transform
if i take the inverse laplace transform i get the result from the characteristic equation
are my steps correct?
thanks for any help