MTH302 Midterm Past Paper 2006

MTH401 · Final Term Examination – Spring 2006 · Time Allowed: 150 Minutes · Marks : 5 · Q

Determine the singular points of the differential equation and classify them as regular or irregula . r

9) 3) x y x y y

Q2. Marks : 10

Solve the given Bernoulli equation

dy y y dx

Marks : 2

Q

Which of the following is singular point of the equation 1) xy xy x y = 0

x = 0 x = 2 x = 1

Marks : 10

Q

ind the eigen value and eigen vector of the following system of linear differential equation F

X X

Q5. Marks : 10

Find solution of the differential equation

y y

x . in the form of a powers series in

Q6. Marks : 2

The non-trivial solution of the system exists only when

det( A I λ

• True
• False

Marks : 2

he form of the particular solution for the differential equation

Q

x y y x e T is

x p y Ae B x B

x p y Ax B e

x p y Ax Bx C e

None of above

Marks : 10

Solve the following homogeneous system of differential equations

Q

t

t dx dy x e dt dt

dx dy x e dt dt

(J ust find the general solution of the equation).

Marks : 5

Solve the differential equation

Q

y y y

Q10. Marks : 2

Which of the following is Legendre’s Equation

(1 dy dy x x y dx dx

(1 dy dy x x y dx dx

(1 d dy x y dx dx

All of three equations are legendre's equation

Q11. Marks : 2

The differential equation (2 (4 xy x dy x xy xy dx is

Separable

Exact

Linear

Bernoulli’s