MCQs of Series Solutions of ODEs and Special Functions (Mathematics - II - 3110015)

Showing 31 to 30 out of 40 Questions

31.

For the D.E.

(x^{2} + 1) y^{''} - 6 x y^{'} - 4 y = 0, \forall x \in ℝ

are ....... points.

32.

....... is series solution of

\frac{d y}{d x} = 0

33.

For the D.E.

(x^{2} - 9)^{2} y^{''} + (x - 3) y^{'} + 2 y = 0

a regular singular point is ........

34.

For the D.E.

(x^{2} - 9)^{2} y^{''} + (x - 3) y^{'} + 2 y = 0

an irregular singular point is .....

35.

In Frobenius Method, the series solution of any D.E. around regular singular point

x = x_{0}, x_{0} \neq 0

assumes the form .......

36.

In Frobenius Method, for solving D.E., the equation formed by equating to zero the coefficient of the lowest power forms in

x

is called ......

37.

In Frobenius Method, the equation formed from the coefficient of the highest powers of

x

is called……….

38.

In the series solution of a D.E. by Frobenius logarithmic term always present in the answer when the roots of an indicial equation are……..

39.

The true statement of following for the power series

f (x) = \sum_{k = 0}^{\infty} a_{n} (x - x_{0})^{n}

......

(a)	The series only converges to $x = x_{0}$
(b)	The series converges for all $x$
(c)	The series converges for $\|x - x_{0}\| < P &$ diverges for $\|x - x_{0}\| > P, w h e r e P \in ℝ^{+}$
(d)	All of the above

40.

For the D.E.

(x^{2} + 1) (x - 4)^{3} y^{''} + (x - 4)^{2} y^{'} + y = 0

, the singular points are ......

Showing 31 to 30 out of 40 Questions