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C 20648 (Pages : 3) फिज्ला16.....५०५०००००००००००००००«००«०००००००००००००००

SIXTH SEMESTER U.G. DEGREE EXAMINATION, MARCH 2022
(CBCSS-UG)
Mathematics
MTS 6B 13—DIFFERENTIAL EQUATIONS
(2019 Admissions)
Time : Two Hours and a Half Maximum : 80 Marks
Section A

Answer at least ten questions.

Each question carries 3 marks.

All questions can be attended.
Overall Ceiling 30.

d
1. Find the general solution of the differential equation + =—ay+b where a,b are positive real
numbers.

2. Determine the values of r for which e” is a solution of the differential equation y'" —3y" +2, =0.

0
3. Using method of integrating factors solve the differential equation ர —2y=4-t.
4. Find the solution of the differential equation :

dy _3x7+4x+2
ಯ. 20-32

(0) = -1.
5. Find the Wronskian of the functions cos? 0,1 + ९08 (20).

6. Find the general solution of the differential equation y"+2y'+2y=0.

7. Let y=$(x) bea solution of the initial value problem :
(1+2? ‏ود2 + ار(‎ + 5 = 0, + (0) = 0,2/(0) = 1.

Determine (/"(0).

8. Determine a lower bound for the radius of convergence of series solutions about each given point

30 - 4 for the given differential equation y"+4y'+6xy =0.
Turn over

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