MTH401 Midterm Subjective 2011

Rana Abubakar Khan

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JOIN FB GROUP FOR VU HELP · MTH401 Midterm Solved Subjective Paper · Paper#01 · MTH 401 May 19, 2011

1. modification of logistic equation (2 marks)lec-12

ln p ap bp

dx dt p ap b p

2. Auxiliary equation for DE x

y y y e

(2 marks)

x sol

m m e

(3)harmonic motion x(t)=c1coswt +c2sinwt write into alternative form (3 marks)lec-22

Solution:

paper#02

my today's mth401 paper

1. .write all the forms of g(x) in the method of undetermined coefficients where g(x) is rght hand

side of Non-homogeneous linear differential equation ?

solution:

n n

o n n n

n n d y d y dy

a a a a y G x

dx dx dx

Q2. Deduce the special use of logistic Equation "Epidemic Spread"?

Solution:

people who infected

y people who not infected x t

t

dy

kxy

dx

x y n

y n x

dy

kx n x

dx

3. what will be the auxiliary Equation of 2nd order Homogeneous Linear Differential equation by

taking solution of exponential form

'' 2 ' t t

y y y e

sol

m m

4. .find the auxiliary equation for the differential equation

''' 2 '' 21 ' 18 t

y y y y e

sol

m m m m

m m m

5. Define general linear equation of order n ?lec 2

n n o a t y n a t y n a y a t y h t

paper#03

My Today Paper MT H401 (Dated 04-12-2011)

Q1. Define cycle of a vibrating body

(2)

Answer: I n travelling from x=A to x=-A,then back to A the vibrating body completes one vibration or

one cycle.

Q2. Construct the auxiliary equation of the following differential equation:

d dx dy dx

Solution:

m m

Q3. Solve the following intial value problem

m dT

K dt T T

T T 