MTH401 Midterm Past Paper Spring 2007 Session 4

MIDTERM EXAMINATION

SPRING 2007 MTH401 - DIFFERENTIAL EQUATIONS (Session - 4 ) Marks: 40 Time: 90min

Student Name:

Center Name/Code:

Exam Date: Friday, May 18, 2007

Question

Q1. (3 (1 marks)

2) x y dx x y dy is Exact

Linear

Separable

Q2. The assumed particular solution for the U.C(Undetermined Coefficient) differential equation (1 marks)

2 x y y = x e is

x p

y · c e · c x

x p y Ax B e

x p y Ax Bx c e

Q3. 2 ln (1 marks)

dy x y y x dx +

is an example of

Separable

Exact

Q4. For the differential equation (1 marks)

y xy x

Integrating factor is

2x

xe x

e−

x

Q5. dy (1 marks)

x y dx x y

Identify the ordinary differential equation

Separable

Exact

Q6. Solve the differential equation (5 marks)

dy y dx x

Q7. Solve (10 marks)

tan ) (tan 2 ) ySec x Secx x dx x y dy

Q8. Find the equation of orthogonal trajectories of the curve (10 marks)

x · y · cx

Q9. Solve the differential equation by method of variations of parameters (10 marks)

tan sec d y y x x dx