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 = 3x²e^2x 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

(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}-

dx² dx    x

d² y    dy

- 4 + (4x - 3) y = e^x by removing

the first derivative.

11. Solve : (x - 1) ^dyy - x + y = (x - 1)² by the

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

^d2^y + y = 6 cos2t given that y = 3, = 1, when t = 0.

.² -'^f

dt

3    UG-315

Attachment: tamil-nadu-open-university--tnou--2008-b-sc-mathematics-49092-1.pdf

Earning:   Approval pending.