anonymous
  • anonymous
Find particular solution to differential equation. 5y'(t) + 10y(t) = 2e^-t
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Are you familiar with method of integrating factor?
anonymous
  • anonymous
I used to be (; I will look it up.
anonymous
  • anonymous
I'll get you started! \[p=10\]\[P= \int\limits 10~dt\]\[\mu = e^P\]

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anonymous
  • anonymous
Oops, I made a stupid mistake. Coefficient in front of the second order derivative must be 1! \[\large p=5\]\[\large P=\int\limits 5~dt\]\[\large\mu=e^{5t}\]\[\large e^{5t}(y'+2y)=\frac{ 2 }{ 5 }e^{-t}e^{5t}\]\[\large (e^{5t}y)'=\frac{ 2 }{ 5 }e^{4t}\]
anonymous
  • anonymous
Continue to solve for y!
anonymous
  • anonymous
Shouldn't it be e^2t * y = Integral (e^2t)(2/5)(e^-t) so y = (2/5)e^-t
anonymous
  • anonymous
Yes, I'm sorry again, I can't even simple math XD I was up 'till 6am studying for an engineering statics midterm I had today. But you are correct! \(\large (e^{2t}y)'=\frac{ 2 }{ 5 }e^{t}\) Don't forget the \(+C\)! :)
anonymous
  • anonymous
Thanks for your time!!
anonymous
  • anonymous
You are most certainly welcome! X)

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