Tamil Nadu Open University (TNOU) 2009-1st Year B.Sc Mathematics "DIFFERENTIAL EQUATIONS " UG 477 BMS 13 - Question Paper

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UG-477    BMS-13

B.Sc. DEGREE EXAMINATION -JANUARY 2009.

First Year Mathematics DIFFERENTIAL EQUATIONS

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 + 9) y = e^2x + 2x².

3.    Solve : (D² - 4D + 3) y = e^x.cos2x .

4.    Eliminate the arbitrary functions / and g from the equation z = f (x + ay) + g (x - ay).

5.    Solve : x (y² + z) p - y (x² + z) q = z (x² - y²).

6.    Solve : p^s = qz .

PART B (5 x 10 = 50 marks)

Answer any FIVE questions.

Solve : (y⁴ + 2y) dx + (xy³ + 2y^A - Ax) dy = 0.

10. Solve : x² - 3x -5y = sin (logx).

dx    dx ^J V B '

11.    Solve the equation

(x - 1) -x + y = (x- l)² dx dx

by the method of variation of parameters.

12.    Solve :

(1 + x + x²) + (3 + 6x) 4- + ⁶ T- = 0

dx² dx

13. Solve : 2xz - px² - 2qxy + pq = 0 .

14. Solve : z⁴q² -z²p = 1

16. Using Laplace transforms, solve the equation y⁽²⁾ + ty' - y = 0 when y (0) = 0, y' (0) = 1.

3    UG-477

Attachment: tamil-nadu-open-university--tnou--2009-b-sc-mathematics-49069-1.pdf

Earning:   Approval pending.