Differential Equation BS 3 Semester/Term UOS — University of Sargodha 2017

University of Sargodha

BS 3rd Term Examination 2017.

Subject: Computer Science Paper: Differential Equation (MATH : 2215)

Time Allowed: 2:30 Hours Maximum Marks: 80

Note: Objective part is compulsory. Attempt any four questions from subjective part

Objective Part (16 x

2)

Q.1

i. Verify that y = 6/5 - 6/5 e^-20x is the solution of Differential Equation dy/dx + 20y = 24

ii. Define the mathematical model

iii. Find the general solution of higher order differential equation. d^4y/dx^4 - 7 d^2y/dx^2 - 18y = 0

iv. Solve the Differential Equation dp/dt = p - p^2

v. Define the Explicit Solution of Differential Equation.

vi. Find the value of K so that the differential Equation (y^3 + kxy^4 - 2x)dx + (3xy^2 + 20x^2y^3)dy = 0 is an exact

vii. Define the linear Differential equation

viii. Solve the Differential equation dy/dx = 5y

ix. What is annihilator operator

x. Determine whether the set functions: f1(x) = x, f2(x) = x - 1, f3(x) = x + 3 is lineeraly independent

xi. Define homogeneous equation give an example

xii. Solve the Differential equation: dy/dx = 1 + e^y-x+5

xiii. Write the linear system of equations: dx/dt = 4x - 7y, dy/dt = 5x in Matrix form.

xiv. Solve the Differential equation x^2 dy/dx + xy = 1

xv. If y1 = x sin(ln x) is a solution of Differential Equation x^2y'' - xy' + 2y = 0 Find y2

xvi. Verify that the Differential Operator D^2 + 3D - 10 annihilate the Function y = e^2x + 3e^-5x

Subjective Part (4 x

12)

Q2. Solve the Differential equation using y'' - 4y' + 4y = (x + 1)e^3x

Q3. Find solution of Differential Equation (x^2 + 1)y'' + xy' - y = 0

Q4. Solve the Differential Equation y'' + 2y' + y = sin x + 3 cos 2x

Q5. Solve the system of Differential Equations dx/dt = 4x + 7y, dy/dt = x - 2y

Q6. Solve the Differential Equations x^2y'' - 3xy' + 4y = 0, y(1) = 5, y'(1) = 3

Q7. Solve the Differential Equations (x + 1)dx + (2xy + x^2 - 1)dy = 0