# Ordinary Differential Equations Past PapersĀ

[OBJECTIVE]

Subject: Mathematics A-IV (Ordinary Differential Equations)

Time Allowed: 10 Minutes

Maximum Marks: 10

NOTE: Attempt this Paper on this Question Sheet only. Please encircle the correct option. Division of marks is given in front of each question. This Paper will be collected back after expiry of time limit mentioned above.

Part-I Ā Encircle the correct option, cutting and overwriting is not allowed. (10)

[SUBJECTIVE]

Subject: Mathematics A-IV (Ordinary Differential Equations)

Time Allowed: 2 Hours 45 Minutes

Maximum Marks: 50

NOTE: ATTEMPT THIS (SUBJECTIVE) ON THE SEPARATE ANSWER SHEET PROVIDED.

Part-II Give short details of each of them, each answer carries equal marks. (20)

Q#1: Describe the following

(a) Differential EquationĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā  (b) Explicit SolutionĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā  (c) Exact Differential Equation

Q#2: Determine the following functions are linearly independent or dependent on [-ā,ā]

f1(x) =x2 f2(x) =X2, f3(x) = 4x-3x2,

Q#3: Solve the following differential equation

X2y1+x (x+2)y =ex.

Q#4: Solve the following differential equation

Q#4: Solve the following differential equation subject to the initial conditions

2yn + 3y-2y = 14x3 – 4x – 11, y(0) =0, y'(0) = 0.

Q#5: Find the power series solution of the following differential equation

yn +(cosx)y=0.