MCQs of Ordinary Differential Equations of Higher Orders (Mathematics - II - 3110015) | GTU MCQ

Mathematics - II (3110015) MCQs

MCQs of Ordinary Differential Equations of Higher Orders

Showing 1 to 10 out of 44 Questions

1.

How many solution(s) does equation

D^{n} y + a_{1} D^{n - 1} y + a_{2} D^{n - 2} y + . . . + a_{n} y = R (x)

have?

(a)	$n$
(b)	one
(c)	two
(d)	none

2.

Suppose auxiliary equation have complex roots

m = p \pm i q

, then

y_{c} =

.......

(a)	$e^{p x} (c_{1} \cos (q x) + c_{2} \sin (q x))$
(b)	$e^{p x} (c_{1} \sin (q x) + c_{2} \cos (q x))$
(c)	$c_{1} e^{(p + i q) x} + c_{2} e^{(p - i q) x}$
(d)	All of above

3.

Which is the correct option, if roots of auxiliary equation are

1, - 1, - 1, 1 \pm 2 i

.

(a)	$c_{1} e^{x} + c_{2} e^{- x} + c_{3} e^{- x} + e^{x} (c_{4} \cos (2 x) + c_{5} \sin (2 x))$
(b)	$c_{1} e^{x} + c_{2} e^{- x} + c_{3} x e^{- x} + e^{x} (c_{4} \cos (2 x) + c_{5} \sin (2 x))$
(c)	$c_{1} x e^{x} + c_{2} e^{- x} + c_{3} e^{- x} + e^{x} (c_{4} \cos (2 x) + c_{5} \sin (2 x))$
(d)	$c_{1} e^{x} + c_{2} e^{- x} + c_{3} e^{- x} + x e^{x} (c_{4} \cos (2 x) + c_{5} \sin (2 x))$

4.

Solution of

y^{''} - 6 y^{'} + 9 y = 0

is ......

(a)	$(c_{1} + c_{2} x) e^{3 x}$
(b)	$(c_{1} + c_{2} x) e^{- 3 x}$
(c)	$c_{1} e^{3 x} + c_{2} e^{- 3 x}$
(d)	None

5.

Which of the following is the general solution to

\frac{d^{2} y}{d x^{2}} + 10 \frac{d y}{d x} + 25 y = 0

?

A & B

are constants.

(a)	$y = A e^{- 5 x} + B e^{- 5 x}$
(b)	$y = A x e^{- 5 x} + B e^{- 5 x}$
(c)	$y = A e^{5 x} + B e^{5 x}$
(d)	$y = A x e^{5 x} + B e^{5 x}$

6.

Which is the correct expression for the complementary function solution of

\frac{d^{2} y}{d x^{2}} + 2 \frac{d y}{d x} + 2 y = 0

?

(a)	$y = A e^{- i t} + B e^{i t}$
(b)	$y = A e^{- t}$
(c)	$y = (A t + B) e^{- t}$
(d)	$y = A e^{(- 1 - i) t} + B e^{(- 1 + i) t}$

7.

Which of the following is solution of

\frac{d^{2} y}{d x^{2}} - 7 \frac{d y}{d x} + 10 y = 0

?

(a)	$y = A e^{2 x} + B e^{5 x}$
(b)	$y = A e^{4 x} + B e^{7 x}$
(c)	$y = \sin (x) + \cos (x)$
(d)	$y = \sin (x) - \cos (x)$

8.

Solution of

(D^{2} + 1) y = 0

is ...... . Where,

D \equiv \frac{d}{d t}

(a)	$c_{1} \cos (x) + c_{2} \sin (x)$
(b)	$c_{1} \cos (t) + c_{2} \sin (t)$
(c)	Both
(d)	None

9.

Solution of

(D^{3} + 8) y = 0

is .......

(a)	$c_{1} e^{- 2 x} + e^{x} [c_{2} \cos (\sqrt{3 x}) + c_{3} \sin (\sqrt{3 x})]$
(b)	$c_{1} e^{2 x} + e^{x} [c_{2} \cos (\sqrt{3} x) + c_{3} \sin (\sqrt{3} x)]$
(c)	$c_{1} e^{- 2 x} + e^{x} [c_{2} \cos (\sqrt{3} x) + c_{3} \sin (\sqrt{3} x)]$
(d)	$c_{1} e^{- 2 x} + e^{- x} [c_{2} \cos (\sqrt{3} x) + c_{3} \sin (\sqrt{3} x)]$

10.

Solution of

(D^{3} - D) y = 0

is .....

(a)	$c_{1} e^{x} + c_{2} e^{- x}$
(b)	$c_{1} e^{x} + c_{2} e^{- x} + c_{3}$
(c)	$c_{1} \sin (x) + c_{2} \cos (x) + c_{3}$
(d)	$c_{1} \sin (x) + c_{2} \cos (x)$

Showing 1 to 10 out of 44 Questions