**[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 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 Equation **(b)** Explicit Solution **(c)** Exact Differential Equation

**Q#**2: Determine the following functions are linearly independent or dependent on [-∞,∞]

*f*_{1}(x) =x_{2} *f*_{2}(x) =X^{2}, *f*_{3}(x) = 4x-3x^{2},

**Q#**3: Solve the following differential equation

X^{2}y^{1}+x (x+2)y =e^{x}.

**Q#**4: Solve the following differential equation

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

2y^{n} + 3y-2y = 14x^{3} – 4x – 11, y(0) =0, y'(0) = 0.

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

y^{n} +(cosx)y=0.