॥॥॥॥॥॥॥॥ 7 10250

19.

21.

Module - 4

| ⋅∙ ‏سس تي‎ 2 `
a) Form the PDE by eliminating a, b, c from a? + be + ठ = 1.

92 022 _ 222

95 iff ۲ + ⋅ ∙− −−−−− 2x+y
18) Solve the partial differential equation ‏ہوڈ+ فیچ‎ ay? ‏ھ0‎ *.
0۴
. a) Solve : x (2 - 220 + y (22 - ‏و(2‎ = 2 (x2 ಎ y2).
೫2 ೫2

೫2
0) Solve the partial differential equation ‏کے‎

कह നനു 0,

Module - 5

A tightly stretched string of length ‘a’ with fixed ends is initially in equilibrium
position. Find the displacement u(x, 1) of the string if it is set vibrating by giving
each of its points a velocity ५0 sin(7x/a).

OR

. A transversely vibrating string of length ‘a’ is stretched between two points

A and B. The initial displacement of each point of the string is zero and the initial
velocity at a distance x from A is kx(a — x). Find the form of the string at any
subsequent time.

Module - 6

+ Find the temperature in a laterally insulated bar of length L whose ends are kept

x ,.0>× 2

7 ⋅ ⋅∙∙ ⋅ f x)=
at temperature zero if the initial temperature is f(x) tox ٢۸9 200 ‏۹ے‎

OR

. Aninsulated rod of length L has its ends A and B maintained at 0° © and 100° ©

respectively until steady state conditions prevails. If B is suddenly reduced to
0° C and maintained at 0° C, then find the temperature in the rod ata distance x from
A at time t.

11

11

10

10

10

10