The PDF(page 3) I am looking at for the method of undetermined coefficients says the following:
For the problem: $$ay'' + by' + cy = f(x)$$
Differentiate the atom f(x) repeatedly. Isolate independent functions whose linear combinations are the derivatives. Multiply them by undetermined coefficients d1, d2, . . . , dk to define an initial trial solution.
What exactly is meant by differentiate f(x) repeatedly? How many times exactly, is it 2 because it's second order? Infinitely? (How could I solve for an infinite number of coefficients) They don't define k so it's not clear how many times I should differentiate