Question is Solve using laplace transform i need someone to clarify the notation i dont get the liimits

y'' − y' − 6y = 0 for {0 < t < 2 ; e^t for t > 2}, y(0) = 3, y0(0) = 4

i dont get whats after the brackets

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- July 13th 2009, 10:31 PMzangestu888Solve differnetial eqation laplace transforms
Question is Solve using laplace transform i need someone to clarify the notation i dont get the liimits

y'' − y' − 6y = 0 for {0 < t < 2 ; e^t for t > 2}, y(0) = 3, y0(0) = 4

i dont get whats after the brackets - July 13th 2009, 11:16 PMCaptainBlack
The right hand side of the equation is a piece wise defined function which is 0 for and for , so you could write this as:

where is Heavyside's unit step (note it does not matter that is apprears to now be defined for , that part of the solution is not relevant).

CB - July 14th 2009, 04:00 PMRandom Variable
I'll give it a try.

You want to put in the form .

because then

EDIT:

so

I'm much more confident this time because I get the same answer when I break up the problem into two differential equations with different initial conditions. - July 14th 2009, 08:36 PMzangestu888
thanks!! i did it also from scratch i got the same answer! except took me a while with stupied mistakes

- July 14th 2009, 10:05 PMRandom Variable