anonymous
  • anonymous
Hello. I just want to ask a question. In the Methods of Undetermined Coefficients, what if you can't even factor the equation given? Ex: (D^2 +4)y = 12cosx How can you answer this? o.o
Differential Equations
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
Does \(D^2y\) mean the second derivative of \(y\)? I've seen this notation before, but have never worked with it.
anonymous
  • anonymous
If the equation is what I think it is: \(y''+4y=12\cos x\), you would make a guess based on the derivatives present on the left side. If you let \(y_p=A\cos x+B\sin x\), then you have \(y_p''=-A\cos x-B\sin x\). Since there are no sines on the right side, you can simply let \(y_p=A\cos x\), so that \(y_p''=-A\cos x\). So, substituting into the original equation, \[-A\cos x+4A\cos x=12\cos x\\ 3A=12\\ A=4\] So the nonhomogeneous solution is \(y_p=4\cos x\).
anonymous
  • anonymous
well, yes. it is the 2nd derivative of y.

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anonymous
  • anonymous
Now I'll just need the auxillary equation..

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