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# Use power series to solve the differential equation.$(x - 3)y' + 2y = 0$

## $y=\frac{c}{(x-3)^{2}}$

#### Topics

Second-Order Differential Equations

### Discussion

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### Video Transcript

doing great. You're going to solve a problem. Number four. Here we assume the resolution off the phone y equals Sigma Chemical 20 to infinity. See and exist to it, and we differentiated legal that void icicles sigma a naked one to infinity and CNN Express toe end minus one. So we need to solve the differential equation. Takes minus three violation plus two white equal to zero, substituting that we will get like X minus three in do sigma canonical toe one to infinity N. C and access to an minus one plus two sigma and equal to 0 2050. Seeing access to an equal zero sigma a negative one to infinity N. C and excess two and minus three Sigma a nickel toe. Want to infinity M C and access to end minus one plus two Sigma n equals zero to infinity. See and access to an equal to zero minus three Sigma Eneko toe 1 2050 n. C. And access to and minus one plus Sigma n equal to zero teen 50 and plus to see and expressed when equal to zero. Uh, and so like minus three sigma a negative zero to infinity and plus one seeing plus one expressed when Plus Sigma and they go to zero to infinity and plus two seeing access to an equal to zero. So the it will come like Sigma and I go to zero to infinity and plus two seeing minus three, 10 plus one see and plus one access to n equals zero for the song Toby zero, We Need Life and plus two scenes. Three into endless one c n plus one equals zero c n plus one necklace and plus two divided by three and do n plus one dot c so they can't right like See, you know will be unknown. So see one equal to zero plus two. Developed by three into zero plus one into sinner, which is by three C. Note. C two equals one plus two. Developed by three into one less one see one, which is equal. Took one by three c. Note. C three because two plus two divided by three into one plus one C two, which is equal to for by 27 c not then c four equals three plus two. Limited by three into three plus one see took, which is equal to 55 81 c. No foreseeing it was and plus one divided by three rest to N. C. Not so Why equals Sigma and equal to zero to infinity. Seeing access to it, which is ableto see not Sigma n equal to zero to infinity and plus one they were by three days to him into access to it. It is equal to see you, not Sigma and equal to zero p. Infinity X by three holder student Let's say not sigma any Go to zero to infinity and x by three Older parent, which comes to be like C zero Sigma and Nico 20 to infinity X by three For the parents. Yes, C zero Sigma n equals zero p infinity. It's de by be It's off. It's by three. Hold up our end so we will get like C zero indoor one by one minus x by three plus zero x The by the X off one developed by one minus x by three from for which comes to be like please see, not developed by three minus six plus C not x D by B X, off three by three Minus X, which is equal to three into three minus six. See? Not divided by three minus X The whole square was trees, you know, that's developed by three minus six. The whole square. Logistical tau nine C not developed by X minus Trade a whole square, which is see by X minus strata, whole square. So why equals C developed by X minus? Traitor! Who's got? That's the no for question. Thank you.

University of New Mexico

#### Topics

Second-Order Differential Equations

Lectures

Join Bootcamp