Power Series Solution for y'-2y'+y=x, y(0)=0, y'(0)=1

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ODEs: Find the first four terms of the power series solution to the IVP y"-2y'+y=x, y(0)=0, y'(0)=1. To check our answer, we find the solution using the annihilator method and expand the exponential terms into power series.
  1. MathDoctorBob
  2. Mathematics
  3. ordinary
  4. differential
  5. equation
  6. linear
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Комментарии
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Wish can skip this in school.
 Too much brain energy drained.

Channel
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@ghostly65 I definitely can. What did you have in mind? The full power series for that function is a mess. Not impossible though. - Bob

MathDoctorBob
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I pretty much just want to see a general way for doing power series in multiple variables. I saw the series on wolframalpha but would like to understand how it is done. Then what I want to do with that series is integrate indefinately three times. The triple integral of z^(y^x) dx dy dz was given to me as a challenge by a friend but i think it would be a lot easier with the power series.

ghostly
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could you do a video for doing power series of multivariable functions specifically z^(y^x)?

ghostly
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What if you have y''+3xy'-y=0, initial conditions y(0)=2 and y'(0)=0? I'm getting strange results

kurtrenner