MTH401 Midterm Past Paper Spring 2006 Session 1

FINALTERM EXAMINATION

FALL 2006 MTH401 - DIFFERENTIAL EQUATIONS (Session - 1 ) Marks: 53 Time: 120min

Student Name:

Center Name/Code:

Exam Date: Monday, February 12, 2007

Q2. Do not ask any question about the contents of this examination from anyone.

1. If you think that there is something wrong with any of the question, attempt it to the best of your understanding.
2. Calculator is allowed.

Question

Question Marks

Q1. If the variation of the path of the curves can be describrd by the concept of differential equations then which of the following differential equation describe the path for y (2 marks)

axis · dy · dx = · dy · dx = · dy · dx = − · dy · dx = ∞

Q2. Suggestive form of the constant input function for the non homogeneous differential equation under the (2 marks)

method entitled as "Method of the undetermined coefficient" is

x

f x · e · f x · a

ax

f x · e · ACosx · BSinx

Suggestive form is impossible.

Q3. Which of the following function is linearly dependant to the exponential function (2 marks)

x

e ?

xe

x

e−

x

xe

x

xe−

Q4. Eigen values for the system of the differential equations X (2 marks)

AX

are evaluated for the

Solution vector

X

Coefficient matrix A

Differentiated solution vector X ′

Transpose of the Coefficient matrix A

Q5. Fundamental set of the solution vectors (2 marks)

for any system of the differential n

X X

X

equations are obtained by

Developing the singleton set

, n

n

X · c X c X · c X

of the linear combinitions of the solution vectors.

Taking derivative of the each solution vector and forming the set

n

X · X · X