University of Sargodha BS 3d Term Examination 2016 Paper: Differential Equation (Math 2215) Subject: Computer Science

University of Sargodha

BS 3d Term Examination 2016

Paper: Differential Equation (Math 2215)

Subject: Computer Science

Time Allowed: 2"30 Hours

Maximum Marks: 80

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

Objective Part (16 x2)

Q.1

1. Verify that y = $

USta define the mathematical model

e-20x is the solution of Differential Equation

+ 20y = 24

com

Find the general solution of higher orden differential equation.

iv. Solve the Differential Equation

v. Define the Explicit Solution of Differential Equation.

- 7"*y

dx=

- 18y = 0

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vi.

Find the value of K so that the differential Equation

(v + kxy* - 2x)dx + (3xy? + 20x}y3)dy = 0 is an exact

vil.

Define the linear Differential equation

vili.

Solve the Differential equation

dx

= 5y

ix. What is annihilator operator

x.

Determine whether the set functions: fi (x) = x, f(x) = x - 1, f(x) = x + 3 is lineeraly

independent

xi.

Define homogeneous equation give an example

xii. Solve the Differential equation:

dy = 1 + ey-x+5

dx

xili. Write the linear system of equations: * = 4x - 7y, a% = 5x in Matrix form.

xiv. Solve the Differential equation x? dy + xy = 1

If ys = x sin(In x) is a solution of Differential Equation x?y" — xy' + 2y = 0 Find yz

xvi. Verify that the Differential Operator D' + 3D - 10 annihilate the Function

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y = e?x + 3e-5x

Subjective Pa0d(4 ×

12)

Q2.

Solve the Differential equation ysige n

y" - 4y' + 4y = (x + 1)e3x

Q3.

Find solution of Differential Equation

(x+1)y"+ xy' - y = 0

Q4.

Solve the Differential Equation

Q5.

Solve the system of Differential Equations

= 4x + 7y,

= x - 2y

Q6.

Q7.

Solve the Differential Equations x'y" - 3ху' + 4y = 0, y(1) = 5, y'(1) = 3

Solve the Differential Equations (* +

1) disit Website: UStadni.com