Laplace transform for an ODE

  • Thread starter manenbu
  • Start date
  • #1
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Homework Statement



Using laplace transform, solve:

[tex]
y'' - y = \frac{x^2-3x+2}{|x^2-3x+2|}[/tex]

y(0)=y'(0)=0

Homework Equations





The Attempt at a Solution



Just to know if I'm on the right path -
Since the quadratic has 2 roots, at 1 and at 2, the entire thing can be equal to either 1 or -1, depends on x.
So can I write it as:
[tex]y'' - y = 1 -2u_{1}(x) + 2u_{2}(x)[/tex]
?


Will this be correct?
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
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Are [itex]u_1(x)[/itex] and [itex]u_2(x)[/itex] supposed to represent the Heaviside step functions

[tex]u_1(x)=\left\{\begin{array}{lr}0, & x<1 \\ 1, & x\geq 1\end{array}\right. \;\;\;\;\;\;\;\;\; u_2(x)=\left\{\begin{array}{lr}0, & x<2 \\ 1, & x\geq 2\end{array}\right.[/tex]

???

If so, you need to be careful to exclude the two roots from the Domain of your final solution since [itex]y''-y[/itex] is indeterminant there. Other than that, it looks good to me.
 
  • #3
103
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Yes, this is exactly what I meant.
Thank you - just making sure I wasn't doing something stupid.
 

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