- #1
sydneyfranke
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- 0
Homework Statement
Find general solution to:
xy''+2y'+4xy=0
Homework Equations
Frobenius Method or Bessel's Equation
The Attempt at a Solution
I know how to get the roots for this problem (which are r1 = 0 & r2 = -1). But not I don't know what to do with these roots. I know that this is considered "Case 3", but I seriously don't know what to do from here.
Furthermore, I have attempted to solve for y1(x) and came up with the answer:
y1(x) = a0(x^-1)cos(2x) + ((a1)/2)(x^-1)sin(2x)
If this is right, then I'm not sure what the next step is. Do I do reduction of order? I hope not because that would take FOREVER.
Wolfram Alpha has the general solution as
y= (c1(exp(-2ix)))/x - (ic2(exp(2ix)))/4x
I'm totally lost. Any help would be appreciated.