anonymous
  • anonymous
how do i find the two power series solutions of y"-2y'+y=0
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
you assume: \[y=\sum_{k=0}^{\infty}A _{k}x^{k+r}\]
anonymous
  • anonymous
now differentiate it for y' and y'' and plug it into the equation.
anonymous
  • anonymous
Could you please clarify the method in steps. Thanks.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
so i wrote what is y. now for y': \[y' = \sum_{k=0}^{\infty}(k+r)A _{k}x ^{k+r-1}\]
anonymous
  • anonymous
take another derivative and you get y'' then plug all the 3 into the equation
anonymous
  • anonymous
About which point? \(x=0\) ?
anonymous
  • anonymous
|dw:1377857501139:dw|
anonymous
  • anonymous
the polynomial above forms the 'characteristic equation'. Normally (in case where not repeated roots), solutions are y = Ke^Dx, if there is one value of D or y = Ke^Dx + Ce^dx if there is 2 values of d. This often happens when D is determined by a square root which can be either positive or negative square root. Note K, C, D and d are constants. D and d are determined by solving the characteristic equation and K and C are determined with known initial conditions.
anonymous
  • anonymous
Just noticed question refers to power series. Not sure my answer is what you want, although I believe it to be a solution to the differential equation given.

Looking for something else?

Not the answer you are looking for? Search for more explanations.