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 Dny+a1Dn-1y+a2Dn-2y+...+any=R(x) have?
(a) n
(b) one
(c) two
(d) none
Answer:

Option (a)

2.
Suppose auxiliary equation have complex roots m=p±iq, then yc= .......
(a) epx(c1 cosqx+c2 sinqx)
(b) epx(c1 sinqx+c2 cosqx)
(c) c1e(p+iq)x+c2e(p-iq)x
(d) All of above
Answer:

Option (d)

3.
Which is the correct option, if roots of auxiliary equation are 1, -1, -1, 1±2i.
(a) c1ex+c2e-x+c3e-x+ex(c4 cos2x+c5 sin2x)
(b) c1ex+c2e-x+c3xe-x+ex(c4 cos2x+c5 sin2x)
(c) c1xex+c2e-x+c3e-x+ex(c4 cos2x+c5 sin2x)
(d) c1ex+c2e-x+c3e-x+xex(c4 cos2x+c5 sin2x)
Answer:

Option (b)

4.
Solution of y''-6y'+9y=0 is ......
(a) (c1+c2x)e3x
(b) (c1+c2x)e-3x
(c) c1e3x+c2e-3x
(d) None
Answer:

Option (a)

5.
Which of the following is the general solution to d2ydx2+10dydx+25y=0 ? A & B are constants.
(a) y=Ae-5x+Be-5x
(b) y=Axe-5x+Be-5x
(c) y=Ae5x+Be5x
(d) y=Axe5x+Be5x
Answer:

Option (b)

6.
Which is the correct expression for the complementary function solution of d2ydx2+2dydx+2y=0?
(a) y=Ae-it+Beit
(b) y=Ae-t
(c) y=(At+B)e-t
(d) y=Ae(-1-i)t+Be(-1+i)t
Answer:

Option (d)

7.
Which of the following is solution of d2ydx2-7dydx+10y=0 ?
(a) y=Ae2x+Be5x
(b) y=Ae4x+Be7x
(c) y=sinx+cosx
(d) y=sinx-cosx
Answer:

Option (a)

8.
Solution of (D2+1)y=0 is ...... . Where, Dddt
(a) c1cosx+c2sinx
(b) c1cost+c2sint
(c) Both
(d) None
Answer:

Option (b)

9.
Solution of (D3+8)y=0 is .......
(a) c1e-2x+ex[c2 cos3x+c3 sin3x]
(b) c1e2x+ex[c2 cos3x+c3 sin3x]
(c) c1e-2x+ex[c2 cos3x+c3 sin3x]
(d) c1e-2x+e-x[c2 cos3x+c3 sin3x]
Answer:

Option (c)

10.
Solution of (D3-D)y=0 is .....
(a) c1ex+c2e-x
(b) c1ex+c2e-x+c3
(c) c1sinx+c2cosx+c3
(d) c1sinx+c2cosx
Answer:

Option (b)

Showing 1 to 10 out of 44 Questions