MTH401 Midterm Past Papers 2017

Rana Abubakar Khan

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MCQs were eventually easy and they weren't that much hard to solve. Most of the MCQs were from chapter#3-12

2 marks questions:

1. Variations of parameters to find the value of w1
2. Show independence b/w p(x) and g(x)

3 marks questions:

1. To find IF of a differential equation given
2. Showing the equation to prove coefficients(given from chapter 16

5 marks questions:

1. First order linear equation to be solved DE was given.
2. Finding Annihilator operator approach of a given DE

Q1. Y = emx then construct an auxiliary equation for

Q2. The general solution is the combination of which two solution ???

Q3. m2+8m+16 is the solution of d2y/dx2+8dy/dx +16 =0 then find the general solution

Q4. Show the following equation in the form of h(x)=g(y)

Q5. By using the newton law show that

Paper 1:-

Q1. Define cycle of a vibrating body (2)

Q2. Construct the auxiliary equation of the following differential equation

3 d2/dx2 - 4 dy/dx = 0

Q3. Solve the following intial value problem

(Integral sign) dT/ T-Tm = (integral sign) K(dt), T(0) = T0

Q4. Factorize the differential equation D4 – 8d2 + 16 if possible

Q5. Find the wronsktin of the differential equation

Y``` -2y``-18y = 6 + 4-t using variation of parameter and the root of the auxiliary equation is m1 = -3 , m2 = -1 , m3 = 6?

Q6. A radioactive isotope has a half-life of 16 days we have 30 g at the end of 30days, how much radio isotope was initially present?

The solution of the IVP (initial value Problem) is given by A (T) = A0 ekt , where K = Ln2/ 16 Paper 2:-

Q1. Define super position principle of particular solution non Homogeneous Linear deferential equation?

Q2. If a mass weighing15lb stretches a spring 3ft then fid K using hook’s law?

Q3. what is an auxiliary equation of a Homogeneous differential equation .also give its two examples.

Q4. what is the general solution of deferential equation?

Q5. Take a deferential equation

d y dy a b cy dx dx + + = we take its exponential solution mx y = e , by putting the above solution we get equation ( ) 2 0 mx e am + bm+ c = . What will be its general solution if roots are distinct real roots?

Q6. Find the complementary solution for the equation ( ) 2 3 2 1 x y¢¢ ? y¢ + = x + e

Paper 3:- MTH401 Q.No.1) Define super position principle of particular solution non Homogeneous Linear deferential equation? MTH401 Q.NO.2) If a mass weighing15lb stretches a spring 3ft then fid K using hook’s law? vuzs MTH401 Q.No.3) what is an auxiliary equation of a Homogeneous differential equation .also give its two examples.

Paper 4:-

Q1. 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 ?

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

Q3. 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

Q4. find the auxiliary equation for the differential equation

y'''-2y''-21y'-18y=3+4e-t