anonymous
  • anonymous
Diff EQ: Show that y_1(t) = t^(-1/2)sin(t) and y_2(t) = t^(-1/2)cos(t) are solutions to the homogeneous problem x^2y'' + xy' + (x^2 - .25)y = g(x). Also find a particular solution to the non-homogeneous problem where g(x) is an arbitrary cont. function.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
replace t with x in the first sentence
anonymous
  • anonymous
Well for the first part, just plug them into the equation, replacing g(x) with 0, and demonstrate that it works.
anonymous
  • anonymous
I thought thats what was going to happen for the first part, what about the second part?. Not sure about the non-constant coefficients.

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Jhannybean
  • Jhannybean
@dan815 @jim_thompson5910 @whpalmer4
anonymous
  • anonymous
Just to clarify: Do you mean \(g(x)\) is a continuous or constant function?
anonymous
  • anonymous
@satellite73 ??
anonymous
  • anonymous
g(x) is continuous
anonymous
  • anonymous
@Directrix
thomas5267
  • thomas5267
Maybe this will help? I am really tired right now and cannot think straight. http://tutorial.math.lamar.edu/Classes/DE/NonhomogeneousSystems.aspx

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