True-False practice, Ch 6, Diff Eq's.

These are just for practice and don't affect your grade. I'm assuming you've read over Ross, Ch 6, on Series Solutions to DE's.

For this quiz, "Power series" implies that every exponent is a non-negative integer. L.I. means "linearly independent". Some questions refer to -

DE #1 : (x-1)y ' ' + xy ' + y/x = 0

DE #2 : x²y ' ' - xy ' - (x²+5/4)y = 0

Fact: x = 0 is a regular singular point of DE #2, and the indicial equation has roots 5/2 and -1/2.

True False. If a power series converges to 0 on an interval, then every coefficient is zero.

True False. Every polynomial is an analytic function.

True False. In class, we solved a DE at an irregular singular point.

True False. DE #1 (above) has only one regular singular point.

True False. DE #1 has two L.I. power series solutions converging near x = 2.

True False. Between any two roots of J₀ there is a root of Y₀.

True False. Every Bessel function of order 0 has a horizontal asymptote.

True False. Bessel's equation of order p has a regular singular point at x=0.

True False. DE #2 has two LI power series solutions at 0.

True False. The gamma function is an increasing function on the positive real numbers.

^{^{Written by S.Hudson 11/02}}