Yes.Use:
Rationalize[0.5, 0] (*1/2*)
Error messages says, you don't uses exact numbers(polynomial coefficients).Use: 1/2 not 0.5.
Plot[DifferentialRoot[ Function[{y, x}, {-y''[x] + 1/2*y[x] == 0, y[1] == 3, y'[1] == 1}]][x], {x, 0, 1}]
Then works.
Thank you for the reply. Do I understand it correctly that if I would like to have coefficients which are not whole numbers I always need to use Rationalize enviroment for them?