Tamil Nadu Open University (TNOU) 2008 B.Sc Mathematics Differential Equation " UG 315 BMS 03" - Question Paper
UG-315 BMS-03
B.Sc. DEGREE EXAMINATION -JUNE 2008.
(AY 2005-2006, CY 2006 batch only)
First Year
Mathematics
DIFFERENTIAL EQUATION
Time : 3 hours Maximum marks : 75
PART A (5 x 5 = 25 marks)
Answer any FIVE questions.
1. Solve : p2 + 2xp - 3x2 = 0.
2. Solve : (D2 - 4) y = sin2 x.
3. Solve : (D2 - 4D + 4) y = 3x2e2x sin2x .
4. Eliminate the arbitrary constants a and b from z = (x + a) (y + b).
5. Solve: x (y + z) p - y (x + z) q = z( x - y)
6. Solve : 3p2 - 2q2 = 4pq.
sin2 t
Find L
t
s + 3
1
8. Find L
(s2 + 6s + 13)2
PART B (5 x 10 = 50 marks) Answer any FIVE questions.
0 , 2 d2 y dy log x sin(log x) + 1 Solve : x2 2 _ x- + y = -v & y-
9.
dx2 dx x
d2 y dy
- 4 + (4x - 3) y = ex by removing
10. Solve
dx2 dx
the first derivative.
11. Solve : (x - 1) dyy - x + y = (x - 1)2 by the
dx
dx
method of variation of parameters given that x and e x are the particular integrals of the equation without the right hand member.
12. Verify the condition of integrability in the equation
(y2 + yz) dx + (xz + z2) dy + (y2 - xy) dz = 0 and solve it.
13. Solve : z4q2 - z2p = 1.
14. Solve : 2xz - px2 - 2qxy + pq = 0 by Charpit's
method.
15. (a) If
f (t) = sin t, 0 < t <n = 0, n < t <2n
and f (t + 2n) = f (t), then find L[ f (t)].
1
(b) Find L
s(s + 2)3
16. Using Laplace transform, solve the equation
d2y + y = 6 cos2t given that y = 3, = 1, when t = 0.
.2 -'f
dt
3 UG-315
Attachment: |
Earning: Approval pending. |