MTH401 Midterm Solved Part 2 with References

MTH401 Mid term past papers (FILE · part II) solved · By masoom fairy · Note: ·  I could not make Neat File due to Much Load · shedding. ·  There is an other file because of Large size · of this one. · MTH401 Deferential Equations · Mid Term Examination – Spring 2006 · Time Allowed: 90 Minutes

Q1. Marks : 1

The method of undetermined coefficient is limited to homogeneous linear differential equation

True False Page 148

The Method of Undetermined Coefficient

Q2. Marks : 1

In the homogeneous differential equation after substitution v=y/x the equation reduces to.

 Separable differential equation. 

 Exact differential equation. Lecture 5

 Remain homogeneous equation. 

Q7. Marks : 1

If the Wronskian W of three function f(x),g(x),h(x) is zero, what can be said about the dependency of the functions

 May or may not be dependent page 113

 Always dependent   Never dependent 

A Vanishing Wronskian does not guarantee linear dependence of functions.

Q8. Marks : 1

an (x) = 0 If in the differential equation

a (x ) d n y + a (x ) d n −1 y + a (x ) d n −2 y + .... + a (x ) dy + a (x ) y = g ( x)

n dx n n −1 dxn −1 n−2 dxn−2 1 dx for some x I then

I. Solution of initial value problem may not unique. II. Solution of initial value problem may not even exist. III. Solution of initial value problem should exist. IV. Solution of initial value problem is unique.

 I is correct only   I and II are correct   I and III are correct   IV is correct only 

Q9. Marks : 1

Equation of the form dy dx + y = x 2 y2 is called

 First order linear differential equation   Bernoulli equation   Separable equation 