Solving an ODE

  • Thread starter cragar
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  • #1
2,552
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If I wanted to solve this [itex] y''+3iy'+y=cos(2t) [/itex] using undetermined coefficients.
and I make the guess [itex] y=Ae^{2it} [/itex]
then i find y' and y'' and then solve for A. I get that A=-1/9
then I take the real part when I multiply it to Eulers formula.
But when I plug this back in to check it doesn't work.
Is there something weird going on because I have an imaginary coefficient in front of the y'.
 

Answers and Replies

  • #2
798
34
If I wanted to solve this [itex] y''+3iy'+y=cos(2t) [/itex] using undetermined coefficients.
and I make the guess [itex] y=Ae^{2it} [/itex]
then i find y' and y'' and then solve for A. I get that A=-1/9
then I take the real part when I multiply it to Eulers formula.
But when I plug this back in to check it doesn't work.
Is there something weird going on because I have an imaginary coefficient in front of the y'.

Better, try : y = A exp(2it) +B exp(-2it)
with cos(2t) = (1/2)exp(2it) + (1/2)exp(-2it)
 
  • #3
1,800
53
How about even more better:

[tex]y_p=A\cos(2t)+B\sin(2t)[/tex]

slap it in (the DE), equate coefficients, bingo-bango.

Also, nothing (algebraic) changes if not only the coefficients are complex but everything else like y and x are complex too. So don't let the i thing intimiate you. Just use regular ordinary complex arithemetic and muscle-through the algebra like always.
 
Last edited:
  • #4
2,552
3
okay thanks for the advice
 

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