Tamil Nadu Open University (TNOU) 2009-1st Year B.Sc Mathematics " DIFFERENTIAL EQUATIONS "UG 466 BMS 03 - Question Paper
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UG-466 BMS-03B.Sc. DEGREE EXAMINATION -JANUARY 2009.
(AY - 2005-06 and CY - 2006 batches only)
First Year
Mathematics
DIFFERENTIAL EQUATIONS
Time : 3 hours Maximum marks : 75
PART A (5 x 5 = 25 marks)
Answer any FIVE questions.
1. Solve : sinpx.cosy = cospx.siny + p.
2. Solve: ()2 - lj = 2 + 5x .
3. Solve: + 4j = x.cos2x.
4. Eliminate the arbitrary function / from / C2 +y2, z-xy = 0 .
5. Solve : x2p + y2q= 4t + y~j .
6. Solve : -Jp + -Jq = -Jy .
7. Find L |cos2Z_.
s
1
<+3+4
8. Find L
PART B (5 x 10 = 50 marks) Answer any FIVE questions.
4, + x~- + y = 4cos |ogC + x dx
d2y dx 2
9.
10. Solve : 2 + x + = cos dt dt
dx ~dy _ + 2 + j = 0. dt dt
+ 4y = cosec2x by the method of
11. Solve
dx2
variation of parameters.
12. Verify the condition in the equa i(y2 + x2y jiz = 0 and solve it.
of integr ability in the equation is,2y - y3 - y2z jix + iy2 - x2z - x3 jiy +
13. Solve: /? + 3g = 5z + tan -3x .
p2 + q2 -2px - 2qy + 2xy = 0.
15. (a) Using Laplace transform, Evaluate
GO /-, .
rcos6t- cos4t
2s + 1
4 +2\4 1
