Download DU (University of Delhi) B-Tech 5th Semester 6310 Mathematical Physics II Question Paper

Download DU (University of Delhi) B-Tech (Bachelor of Technology) 5th Semester 6310 Mathematical Physics II Question Paper

773i: question paper contains 3 printed pages. Your Roll No. .....................
Sl. No. of Ques. Paper : 6310 F?S
Unique Paper Code : 2341504
Name of Paper : Mathematical Physics F [I
Name of Course : B. Tech. (Computer Science) (FYUP Scheme)
Semester : V
Duration :3 hours _ Maximum Marks ; 75
(Write yaw Roll No. on the mp immediately on receipt of this question paper. )
Do ?ve questions in all. Question No. 1 'is compulsory.
I. Do any ?ve questions :
(a) Detennine the order, degree and linearity ofthe differential equation:
[4?le + d_y + 4 y = x
dx? d x
. (b) V What is Wronskian? Calculate the value of wronskian for:
x? and x? ( In x)
(c) Prove the following property of Poisson Bracket:
' [uv,w]=[u.w]v+u[v,w]
(d) Find the extreme points of the function:
f(x,y)=y2+4xy+3x2+x3
(e) Solve:
' (f) De?ne generalised momenm for n-particle system, and ?nd its time
derivative.
(3) Form the differential equation whose only solutions are:
al, a2 xe", 03 x2 e?.
(h) Find the extremal of the integral :
if(zysinx?y")dx,here y' = d:. (sx3=|5)
o d
? 1 PTfo

Ex)
Solve the following differential equations:
d)?-_ 2
(a) ?? ? y tanx ? y secx
dx
dv r?x+1
(b) _)_:_J___
dx y+x+5
Solve the following differential equations:
d 2 y
d x2
- y - xcosx
(8)
d2 d (lnzr)2
2-21 _y_ =___
(b) x dx2 +3xdx +y x
(a) Solve the following differential equatioh
(x? + y?)dx - xy3 dy =0
(b) Using the method of variation of parameters, solve
(D2 +9)y=xsin3x; Ds?
(a) Using the method of undetermined coefficients, solve
d?y dy
?? ? 2? + = ? +
d):2 dx y e x
(b) Solve the coupled differential equations;
?+21= Q+10cost
d: d:
_d_y T 2y ? 434'- d_x
d: d:
(6')
(9)
(6)
.(9)
(6)
(9)
(6)
(9)
(21) Find the equation of the shortest path between two points on the sur-
face of sphere of radius a .
(6)
(b) Using Lagrange?s method of undetennined multiplier, ?nd the max-
imum value of u= x" y" z?when the variablesx,y,
tothecondition ax+ by+ c: = p + ?1 +_ ?-
are subjected
(9)

(a)
(b)
(a)
(b)
F ind the Lagrangian corresponding to the Hamiltonian
_.P2 17.:
H???" +?~ +1: , 6
4a 4b X} H
Using Hamilton?s equations of motion and the expression
L(q,?)=p? 'H(q?p)
prove that: p = g]; and p = ?. (9)
q
Show that
(i) [qjv ?1:qu ?
(ii) [p]! H]= Pp (6)
here, H denotes Hamiltonian and 1 s j S n.
Write the Lagrangian of the system of two masses 2m and m, shown
below in Fig. (1). In this ?gure, y: and y; are the displacements of two
masses from their equilibrium positions. Hence obtain the equations of
motion of these two masses. (9)
Hoe