Question

d^2f/dx^2+(ax+b)df/dx+cf=const

Could someone know an easier way to solute this ode?

Answer 1

reduce to a quadratic and solve for roots by quadratic formula

Answer 2

What do you mean with "reduce to a quadratic " ?

Do you mean, I should transform it in dies form d^2f/dx^2+bdf/dx+cf=const-(ax+b)df/dx .

Answer 3

if you allow the coefficients to be the terms for a quadratic, i.e. \[r ^{2}+(ax+b)r+c = 0\] then use the quadratic formula
\[(-b \pm \sqrt{b ^{2}-4ac})/2a\] to find r such that it satisfies the ODE

Answer 4

but you can't do that because r is also a function of x. r=r(x)

Answer 5

no you treat it as a constant

Answer 6

what do you have so far for your work and/or proof?

Answer 7

I though about another approach, please, have a look on this site,
http://www.ltcconline.net/greenl/courses/204/PowerLaplace/seriesSolutions1.htm

Answer 8

did you figure out the u substitution? if you did then it should follow...but i honestly don't think you need to use series for it

Answer 9

I figure it, but it seems to be really complicatet to have a serie solution.

Answer 10

Because of the non-constant coefficients and it become very ugly

Answer 11

can I send you a copy of my work?

Answer 12

Try uploading a pic to http://imgur.com/ and pasting the link to it here.

Answer 13

yeah i would like to see it

Answer 14

(We'll be adding image upload to OpenStudy soon, I hope.)

Answer 15

You could try using laplace transforms. It would turn the the 2nd order ODE into a 1st order ODE. Usually 1st order ODE are easier to solve. Look at the example here http://tutorial.math.lamar.edu/Classes/DE/IVPWithNonConstantCoefficient.aspx

Answer 16

i think that's what he was trying to do

Answer 17

here is a copy
http://imgur.com/9y7hu

Answer 18

hope u can read it,

Answer 19

ok yeah now it is better to see...

i think that it works, after simplifying then you can solve the ODE. but i think its already simplified...

Answer 20

but when it is already simplified, what is the result now?

Answer 21

I'm gonna use matlab to solve,

Answer 22

you can also check your answer on this website:
http://www.wolframalpha.com/input/?i=y''+%2B+(ax%2Bb)y'%2Bcy+%3D+f

The answer seems a bit complicated :\