anonymous
  • anonymous
this one is tricky. help please! y''-4y'+3y=2cosx+4sinx i'm having trouble getting the Yp!
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
You can try substituting y = asinx + bcosx
anonymous
  • anonymous
why would that help. I'm in diff eq as well and I wasn't thinking about that.
anonymous
  • anonymous
its called th method of undetermined coefficients

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anonymous
  • anonymous
put it on the left side....compare with coeffs on the right fr etermining a a and b
anonymous
  • anonymous
isn't it y=a cos x + b sinx + cx cos x + dx sin x
anonymous
  • anonymous
that is for a special case i think
anonymous
  • anonymous
what are the roots anyway? +i, -i aren't they like, twice? then it will be case 4?
anonymous
  • anonymous
r^2 - 4r +3 = 0 (r - 3)(r-1) r= 3, 1
anonymous
  • anonymous
that is for the homo part
anonymous
  • anonymous
im telling you take y=asinx + bcosx substitute y'' and y' and y in the above eqn and compare LHS and RHS ull get 2 eqns in a and b determine a and b and you have your soln
anonymous
  • anonymous
i did that, i always get 0 for B. it's not supposed to be the answer.
anonymous
  • anonymous
im getting the answer as b=1, a=0 which means y=cos x y=cos x satisfies the above eqns
anonymous
  • anonymous
oh sorry. i looked at the wrong answer on my book. i am sorry. Our answer is right. Thank you!
anonymous
  • anonymous
Your welcome

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