Homogeneous linear DE with constant coefficients

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?

• yes and yes. more characters Aug 16 '15 at 3:53
• Why "yes" on b) ?
– etf
Aug 16 '15 at 7:53
• 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. Aug 16 '15 at 12:07