MTH401 Midterm Solved Subjective 2012-2013

MTH401 27 Feburary · 2012 Final term PAPER SOLVED · TODAY’s Paper · Total Question: 52 · Mcqz: 40 · Subjective question: 12 · 4 q of 5 marks · 4 q of 3 marks · 4 q of 2 marks · Guidelines:

Prepare this file as I included all past papers and current papers (shared

till now) in it. You will have to clear the concepts and formulas of topics

according to which questons are solved in file.

TODAY’s PAPER no 1 · Objective: MCQz · Topic · Number of Mcqz · Ratio Test Convergence · Divergence · D.E(Integrating Factors +Homogenous+linear+bernoli) · Z=

X Z

Reactance & Impedence · Damped Motion · Maxima · Quasi period · Besslen’s Equation · Matrix Type(square+system to matrix · conversion) · Eigen Values+Eigen Vector · Multiplicy of Eigen Vector · Virtual Study Solutions · D.E operator · General Solution · BVP

Please review the formulas of above topics.

Q1. t

t dx dy x e dt dt

dx dy x e dt dt

lec 36 example 1

in decoupled form.

Determinants are

Therefore, in decpoupled form, we get t

t

t

t

t t

t t

t

t

t

t dx dy x e dt dt

dx dy x e dt dt

D x Dy e

D x Dy e

D D e D D e

D D e D D e

D D e D x D D e D

D D D e y D D D e

Q2. Q:10:

Find a series solution for the differential equation y y about

such that

Find condition of cofficent for

n n n n a a c c

Q11. Which series is identically zero?

Q12. A

eigenvalues

Eigenvectors È Í Î

Note: I am not going to solve this question solve it by your self by

consulting two examples below.

========================First Paper End=====================

Q1. Find Coefficient of metrix:

dx x y dt = -