MSc Maths (Difference Equations) 3rd Semester Question Paper 2024-25 Pdf | MSc Maths 2nd Year Question Paper 2025 Pdf

MSc Maths 2nd Year (3rd Sem) Question Paper 2024-25 : Maths MSc 3rd Semester Papers M.Sc 3rd Semester Maths Question Paper 2025

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MSc Maths 3rd Semester Question Paper 2024-25 Pdf

Paper Code: 41174

B-1524

M.A./M.Sc. Mathematics (Semester Third) Examination, 2024-25

Difference Equations

Time: Two Hours ] [Maximum Marks: 70

Note: Attempt all the section as per instructions.

Section-A

(Short Answer Type Questions)

Note: Attempt any three questions out of the following.

Each question carries 10 marks. Answer are required not exceeding 300 words

1. Prove that. +u n =^ n + 1 C 1 .u 0 +^ n+1 c 2 1

2. If z{<f(n)>}F(z) then show that dF(z) z{<nf(n)}=-zdz

3. Solve by method of generating functions: y k + 2 -2y k-1 +y k =2^ k with y_{0} = 2 and y,-1

4. Find z-transform of cosh ((n*pi)/2 + a)

5. State and discuss Lagrange’s identity.

6. Find the difference equation for the given functions. f(x) = a * 2 ^ x + chi * 2 ^ (x + 1)

MSc Maths (Difference Equations) 3rd Semester Question Paper 2024-25 Pdf

Section-B

(Long Answer Type Questions)

Note: Attempt any two questions out of the following.

Each short question carries 20 marks. Answer are required not exceeding 600-800 words.

7. Determine the type of stability of the point (0, 0) of the linear system: d/dt (x) = 4x + 2y + 2x ^ 7 – 3y ^ 2 d/dt (y) = 4x – 3y + 7xy Also, find the general solution of the corresponding linear system and draw its trajectories.

8. Find the generating function of the numeric function a_{r} = 2 ^ r + 3 ^ r ,r>,0

9. State and prove Abel’s formula.

10. Solve the system of difference equations: y k + 1 -y k +2Z k+1 =0 z k + 1 -z k -2y k =2k

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