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B2A102 Pages: 2

8) Solve x3 £2 2 242 + ‏کے برج‎ (6)
b) Solve (D? + 2D — 3)y = e* cosx (5)
Module III
7 ∙ ⊔ ∙∙−−↥⊹∝∣−∏≺∝⋖∘
. a) Find the Fourier series of f(x) = { 1+50 ‏بے‎ aor (6)
8 ४ ⋅ ‏وہ‎ ‰ 0< <> 1
b) Find the half range sine series of f(x) = { छ ~ 1 > ‏ب‎ > 2 (5)
OR
-?, -7 > ‏پر‎ > 0
. a) Obtain the Fourier series of f(x) = | 4! (6)
7/4, 0 > ८ > 1
9) Find the half range cosine series of f(x) =x,0Module IV
.a) Solve (02 -200' + 0/2)2 = சர்‌? + x3 (6)
7 ⋅ ‏ج33‎
‎0) Find the Particular Integral of —>— 7 ನ್‌ ‏تو6‎ = si n(x + 29) (5)
OR
a) Solve (02 + DD' - 60'2)2 = y sinx (6)
b) Solve (mz - ny)p + (nx -—lQq=ly—mx (5)
Module V
Solve the one dimensional wave equation a = cr oe with boundary conditions
u(0,t) = 0,u(l,t) = 0 forall t and initial conditions u(x,0) = 7/൭.) किया
t=
g(x). (10)
OR
A sting of length 20cm fixed at both ends is displaced from its position of
equilibrium, by each of its points an _ initial velocity given by
ചമ 0 > ‏٭‎ > 0 ⋅ ⋅ ∙
{ 20೨% 10displacement at any subsequent time. (10)
Module VI
Derive one-dimensional heat equation. (10)
OR
Find the temperature in a laterally insulated bar of length L whose ends are kept at

temperature 0°C, assuming that the initial temperature is

0 > 2 > 2

)10( نا < ‰ > 1/2 ,= 0(

eK

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