anonymous
  • anonymous
can anyone say how to solve a differential equation using method of undetermined coefficients??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients
anonymous
  • anonymous
give me the equation
anonymous
  • anonymous
ok( D^2-5D+6)y=e^3x+sinx

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anonymous
  • anonymous
just tell me the assumed particular integral.....
anonymous
  • anonymous
bad diff equation, what is D?
anonymous
  • anonymous
D is the notation for operator d/dx....
anonymous
  • anonymous
\[y^{\prime\prime}-5y^\prime+6y=\operatorname{e}^{3x}+\sin x\]
anonymous
  • anonymous
yeah
anonymous
  • anonymous
I think one of the best ways to solve this equation is by using Laplace transformation
anonymous
  • anonymous
in the question it is specifically mentioned to use method of undetermined coefficients
anonymous
  • anonymous
The particular solution will be the sum of particular solutions. Try Ae^(3x) + Bsin(x)
anonymous
  • anonymous
solve for A and B
anonymous
  • anonymous
no it will not work as e^3x is a term in complementary function
anonymous
  • anonymous
particular solution \[y=Ae^{\lambda1 x}+Be^{\lambda2 x}\], lambda are complex numbers
anonymous
  • anonymous
yeah...i just did it and it's a mess...too much to write out...buggin' out and going to bed...good luck.
anonymous
  • anonymous
I thought the others were going to help you. Since e^(3x) is part of the homogeneous solution, try xAe^(3x) as one part. Since you have a trig. function too, add to this Msin(x) + Ncos(x). So try,\[y_p=Axe^{3x}+M \sin x +N \sin x\]
anonymous
  • anonymous
I think I ended up with A=1, M=N=(1/10). Try it.
anonymous
  • anonymous
\[C _{1} e^{2x} + C_{2}e^{3x} +0.1(\cos[x] + \sin[x])+xe^{3x}\]
anonymous
  • anonymous
Yes
anonymous
  • anonymous
thanx i ended up with the same solution guess the answer in the book was wrong

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