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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 nonhomogeneous problem where g(x) is an arbitrary cont. function.
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 nonhomogeneous problem where g(x) is an arbitrary cont. function.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0replace t with x in the first sentence

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well for the first part, just plug them into the equation, replacing g(x) with 0, and demonstrate that it works.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought thats what was going to happen for the first part, what about the second part?. Not sure about the nonconstant coefficients.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@dan815 @jim_thompson5910 @whpalmer4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Just to clarify: Do you mean \(g(x)\) is a continuous or constant function?

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0Maybe 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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