Tamil Nadu Open University (TNOU) 2006 B.Sc Mathematics 1st Year " Differemtial Equation " UG 745 - Question Paper

UG-745    BMS-03

B.Sc. DEGREE EXAMINATION - JUNE 2006. First Year DIFFERENTIAL EQUATIONS Time : 3 hours    Maximum marks : 75

PART A (5 x 5 = 25 marks)

Answer any FIVE questions.

1.    Solve : xp² - 2yp + x = 0.

2.    Solve :(D² + 3D + 2) y = x².

3.    Solve :(D² - 2D + 4) y = e.cosx .

4.    Form a partial differential equation by eliminating the function of <j> from

0 {x + y + z, x² + y² - z²) = 0.

5.    Solve : (mz - ny)p + (nx - lz) q = ly -mx .

6.    Solve : z = px +qy + c*Jl + p² + q² .

7. Prove that L [tⁿ] =    and hence

sⁿ⁺¹

find L [*].

5 + 2

8. Find L~^l

Answer any FIVE questions.

9.    Solve: (2x + l)² y'-2(2x + l)y'-12y = 6x .

10.    Solve: (4D+ 2)x + (9D+ 3l)y= e

(3D + l)x + (ID+ 24)y = 3. d² v

11.    Solve : -5- + 4y = cosec (2x) by the method

dx²

of variation of parameters.

12.    Verify the condition of integrability in the equation (y + z) dx + (z + x) dy +(x + y) dz = 0 and solve it.

13.    Solve: p+3q = 5z + tan (y-3x).

14.    Solve : p³ +q³ = 27z .

15.    (a) Find L [(/()] where

fit) = 0 when 0 < t < 2 = 3 when > 2.

16. Using Laplace transform, solve the equation

d~ v dv    dy

+ 2--3y = sin t given that y = = 0 when

dt² dt dt

t = 0.

3    UG-745

Attachment: tamil-nadu-open-university--tnou--2006-b-sc-mathematics-49081-1.pdf

Earning:   Approval pending.