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..

Thanks ..

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- Jan 3rd 2011, 03:10 AM #1

- Jan 3rd 2011, 06:05 AM #2

- Jan 3rd 2011, 01:28 PM #3

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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.

- Jan 3rd 2011, 05:50 PM #4

- Jan 3rd 2011, 06:07 PM #5

- Jan 3rd 2011, 06:38 PM #6

- Jan 3rd 2011, 11:29 PM #7

- Jan 4th 2011, 03:26 AM #8

- Jan 4th 2011, 03:13 PM #9

- Jan 6th 2011, 03:42 AM #10