A 31101 Pages: 3
PART B
Answer six questions,one full question from each module
Module 1 ∎
↿∍∂⋟⊰≺⊃∣⋁∈⋔⊖↧∎⊓∣∎↥∣∎∂∣∨∂∣∐⊖↾⊃⊺∘⇂⊃↿⊖⋯⋅↖⋎⊔−−∶−−≗∙↿⋅⊳⋅⋅−⊲⊑−∙↴↘⋅∶⊙⋅∙↴↽⊏⊙⋟−−∃↾∙↖↾↙⊏⊙↴⋅−⇀−≤∙ (6)
b) Find the general solution of the differential equation 3" — vy" ~+ 44" = 0 (5)
or
14 ஐ If¥,(<) =~ is a solution to the differential equation
(a+ 2552 - 2: + 2४ = 0, find the general solution. ie?
b) Solve the ordinary differential equation 3 - நோ 4y' + 6y = 0. (5)
Module 11
153 ಖ Solve 2(3x+1)? $4 24(3x+1)S + 18y = 9x (6)
0) Solve (D*+2D?+41)y = x7 (5)
GR
16 ൭) Use method variation of parameiers 10 6 ಇರರ 4 = tan 2x (6)
b) Solve (2 - 42 + 4) = sin x (5)
Module |
17 8) Obtain the half range Fourier cosine series expansion of f(x) = x sin x in (0,7). (6)
b) Find the Fourier series for f(x) = |x|, -1OR
18 8) Pind the Fourier series for f(x) = = = 0 (6)
0) Find the Fourier series of the periodic function f(x) of period 4, where
வற்‌ =
(ടെ 98 tere ட்‌ ©)
0,1 <~ <>
Module 1९
19 8) 50९ ४ + ‏خرس ووو‎ (6)
b) Find the partial differential equation of all planes which are at a constant distance ‏ا۱ے‎
‎k from the origin. இ
08
20 a) Solve x*(v—2)pty7le- ‏ووس وم 3ع = ول‎ (6)

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