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solution.
OR

Reduce to first order and solve )'' + (1 + ಏಂ) =0

Solve the initial value problem 9y” — 30y’ + 25) = 0, y(0) = 327 (0) = 10.
Module 11

Solve ‏“بن‎ ~ 2)" + 5) = e**sinx.

Using method variation of parameters solve y” + 4y = tan2x
OR
Solve 2397 + 3x2y" + xy’ + + =x + logx
Solve using method of variation of parameters )'' - 2)' +y = <
Module 111
Find the Fourier series of periodic functionf (x) = {+ ಇ O vith period
2. Hence prove that 1 + = + = ಡೋ ದ 2
OR
Find the Fourier series of periodic function f(x) = xsinx ,0 < > < 27 with
period 2 7.
Module 1V
Solve p - 205 3x? sin(y+2x).
Solve rt+s-6t=y 5102,
OR

Solve x(y —z)p+y(z—x)q = 2८ - 2).
Solve (02 — 220" — 15D”) z= 1279.
Module V
A tightly stretched string of length L is fixed at both ends. Find the displacement
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 = is initially in a

position given by u = vgsin? (=) ,0
position, find the displacement function u(x, t)

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