# MTH401 Differential Equations Current Mid term paper December fall 2012

Total Questions = 26
Total MCQ = 20
2 Questions of 2 Marks
2 Questions of 3 Marks
2 Questions of 5 Marks
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 ?
2. Deduce the special use of logistic Equation “Epidemic Spread”?
3. what will be the auxiliary Equation of 2nd order Homogeneous Linear Differential equation by taking solution of exponential form y”-2y’+y=et/t2+1
4. Find the auxiliary equation for the differential equation
Y”’-2y”-21y’-18y=3+4e-t
5. Define general linear equation of order n?

Another Paper:

There were 20 MCQ’s
2 Questions of 2 marks
2 Questions of 3 marks
2 Questions of 5 marks
Total Questions(26)

Q1)If the complementary solution of the following non – homogeneous linear differential equation is , then determine its particular solution using Undetermined Coefficients method.
(5 mrks)
Q2)If general solution of Logistic Equation is
with initial condition is P(0)=Po , then find P(t), also find its limiting value? (5 mrks)
Q3)Determine whether the following functions are linearly dependent or linearly
Independent ?
(3 mrks)
Q4)Derive amplitude in the solution of equation of simple harmonic motion? (3mrks)
If the initial temperature of cooling body is then write the differential equation of Newton Law of Cooling .(2 marks)
Q5)Define frequency of vibrating body in simple harmonic motion? (2 marks)
If and are the solutions of , then which of the following is the most accurate option for ?