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Here are some question from book, I have to answer with "yes" or "no":

a) $\phi(x)=x^{2}+3$ is solution of some homogeneous linear DE with constant coefficiens,

b) $\phi(x)=\frac{1}{2+x^{2}}$ is solution of some homogeneous linear DE with constant coefficiens.

Answer on a) should be "yes" (I found DE y'''=0) and "no" on b). Is it ok?

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    $\begingroup$ yes and yes. more characters $\endgroup$ Aug 16 '15 at 3:53
  • $\begingroup$ Why "yes" on b) ? $\endgroup$
    – etf
    Aug 16 '15 at 7:53
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    $\begingroup$ No, yes as in I agree with your "no". The only solutions to constant coefficient ODEs in homogeneous case are just polynomials, exponentials, sines, cosines and products and sums thereof. $\endgroup$ Aug 16 '15 at 12:07

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