Pl help me to solve it..
Solve: , with the initial conditions y(0)=o, y'(0)=1 and y''(0)=0 using Laplace Transform.
I've taken Laplace Transform,
I've simplified it but, I did not get it..
Oh, dear, oh dear, oh, dear! I really dislike the Laplace Transform! It can be used in two diametrically opposite ways- to "look up" solutions to non-homogeneous equations or to assert a form of a solution in very abstract theorems. The first is more easily done in other ways and the second, undergraduates never see.
I would look at that equation and immediately write down it characteristic equation: . It's easy to see, by inspection, that r= 1 is a root of that and that so that r= 1 is a double root and r= -1 is a root. That tells us that the general solution to the associated homogeneous equation is .
The "non-homogeneos" part is . Since is already a solution to the associated homogeneous equation, we try a solution of the form . Then , , and .
Putting those into the differential equation will give you equations for A and B.