anonymous
  • anonymous
Can anyone help with LaPlace transforms?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
y'’ + y = 1, y(0) = 1, y’(0) = 1
nikvist
  • nikvist
\[y''+y=1,y(0)=1,y'(0)=1\] \[L(y''+y)=L(1)\] \[s^2Y(s)-sy(0)-y'(0)+Y(s)=\frac{1}{s}\] \[(s^2+1)Y(s)=s+1+1/s,Y(s)=\frac{s+1+1/s}{s^2+1}\] \[Y(s)=\frac{s^2+s+1}{s(s^2+1)}=\frac{1}{s}+\frac{1}{s^2+1}\] \[L^{-1}(Y(s))=1+\sin{x}\]
anonymous
  • anonymous
Hmm ok lemme see what it looks like compared to mine.

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anonymous
  • anonymous
The second step if you were to write it all out would look like this right?\[s^2L(y)-s f(0)-f(0)-L(y)=L(1)\]
nikvist
  • nikvist
correct is \[s^2L(y)-sy(0)-y'(0)+L(y)=L(1)\]
anonymous
  • anonymous
replace f's with y's right?
anonymous
  • anonymous
We're saying the same thing I'm using f's

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