can anyone solve this y"-(2/x)y'+(1+2/(x^2))y=xe^x

Question

amistre64 · Answer

seems doable ...

amistre64 · Answer

im thinking series ....

anonymous · Answer

no series

amistre64 · Answer

why not?

abb0t · Answer

You can use laplace transform.

amistre64 · Answer

might as well be asking:  can any one open this door?  sure.  um, but without using your hands? ....

abb0t · Answer

LOL!

anonymous · Answer

u see u have two hands use the other one

amistre64 · Answer

without using any methods known to man ... solve it :)

amistre64 · Answer

laplace requires intial conditions i believe

anonymous · Answer

u mean the only method is using series?

abb0t · Answer

avril lavigne, aren't you a singer? Why are you taking differential equaitons?

abb0t · Answer

You can use reduction of order to reduce them to constant coefficients if i remember correctly.

amistre64 · Answer

variation of parameters ... a wronskian .... stuff like that maybe

anonymous · Answer

I myself think it must be some kind of substitution!
looks like one

anonymous · Answer

to use wronskian I need at least one solution

amistre64 · Answer

$$let~y=\sum_0c_n~x^n$$ :)  thats a substitution

abb0t · Answer

http://tutorial.math.lamar.edu/Classes/DE/ReductionofOrder.aspx that's the method i was talking about. reducing it to constant coeff. but there is another method that you don't need to reduce them to constant coeff, but instead a similar method to using annihilators. But i have to go, hope this helps!

amistre64 · Answer

you can develop one solution from the homogenous and then work it into the wronskian ... by chance

anonymous · Answer

that's not a substitution! thats an answer u gave! I don't know how?

amistre64 · Answer

:)

anonymous · Answer

what do u mean by chance?

anonymous · Answer

took diff eq three years ago, don't remember much, bump for review

amistre64 · Answer

i mean that if you can solve the homogenous then you have one of the solutions to apply for the wronskian;  but that rests on the ability to determine the homogenous solution to start with

anonymous · Answer

well that is the primary problem! the rest is pretty simple

anonymous · Answer

reducing to constant coefficient must be the solution but for that I need a good substitution.

anonymous · Answer

You could find the auxiliary equation of the left hand side, then use it to find a general solution (ie complementary function)
Then find a particular solution to rhs
and add them together

anonymous · Answer

well u can't find an exact solution to the right handside without solving $$y_{g}$$ 
sarahusher

anonymous · Answer

u know any general substitutions for reducing