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anonymous

  • one year ago

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.

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  1. anonymous
    • one year ago
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    replace t with x in the first sentence

  2. anonymous
    • one year ago
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    Well for the first part, just plug them into the equation, replacing g(x) with 0, and demonstrate that it works.

  3. anonymous
    • one year ago
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    I thought thats what was going to happen for the first part, what about the second part?. Not sure about the non-constant coefficients.

  4. Jhannybean
    • one year ago
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    @dan815 @jim_thompson5910 @whpalmer4

  5. anonymous
    • one year ago
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    Just to clarify: Do you mean \(g(x)\) is a continuous or constant function?

  6. anonymous
    • one year ago
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    @satellite73 ??

  7. anonymous
    • one year ago
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    g(x) is continuous

  8. anonymous
    • one year ago
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    @Directrix

  9. thomas5267
    • one year ago
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    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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