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solution.
OR
Reduce to first order and solve ‏“بز‎ + (1 + 520") = 0 (5) *
Solve the initial value problem 9y” — 30y’ + 25) = 0, y(0) = 3, ै/ (0) = 10, (6)
Module 11
Solve ‏"بن‎ —2y’ + 5) = e?*sinx. ⊳ (5)
Using method variation of parameters solve y” + 4) = tan2x (6)
OR
Solve x3y"" + 3x2y" + xy’ + + =x + logx (5)
Solve using method of variation of parameters )'' - 2)' +y = ~ (6)
Module 111
Find the Fourier series of periodic functionf(x) = ‏چا سر‎ 5 period 7
2. Hence prove that 1 + = + a + *** "= =
OR
Find the Fourier series of periodic function f(x) = xsinx ,0 > ‏ع‎ > 27 with (11)
period 2 7.
, Module 1५
Solve - 24 = 30 sin(yt2x). (5)
Solve r+s - 61 9५ sinx. (6)
OR
Solve x(y - 27 + (४ - ८) 4 = 2) - 9). (5)
Solve (92 - 2DD' - 15D") 2- 12xy. (6)
Module ५
A tightly stretched string of length L is fixed at both ends. Find the displacement (10)
u(x,t) if the string is given an initial displacement f(x) and an initial velocity g(x).
OR
A tightly stretched string with fixed end points x = 0 and x = 1 is initially in a
position given by u ಇ 7051 (*),0
position, find the displacement function u(x, £)

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