A2100 Pages: 3

differential equation y"—Sy'+4y=0. Can Se*—2e**be a solution(do not use

verification method) of the differential equation? Explain.
OR
Discuss the existence and uniqueness of solution of the initial value problem

oe x+y? ,y(O)=1 inthe rectangle || < 1, 2-1 < 1.
If 11) = is a solution of xy" + 2xy'—2y =0, find the general solution.
Module 1
By the method of variation of parameters, solve y"+ y= xsinx.
Solve 1“ + 51" + 6} = € 1023.
OR
Solve x’p"+xy'-9y= logx.
Solve y"-2y'+5y=x° .
Module 111
Find the Fourier cosine series representation of (६) = ४, 0 < ४ < 7. Also find the
Fourier series representation f(x) if f(x) is periodic function with period ۰

OR
Find the Fourier series of the periodic function f(x) of period 4, where

2, -2 <.*<0
(४) = 0 and deduce that
श ॐ 1 1 1 ர்‌ 1 1 1 7
¢) 1+--+-- +~ +---=--- and (1) 1---+----- +न
பதக அச அர 8 ஸ்‌ ‏بت‎ 4
Module IV
2 2 ©
6 6
Find the particular solution of ಹ ‏کو‎ +2 > = 12.
ox Oxdy இ

Find the general solution of (2 +2°)p—xyq=-Xxz.
OR

Solve (D? +3DD!+2D")z = (2x+y)’.

Oz Oz 62 5

Solve 4— —4 1 16 log(x+2y).
ax? இறு Oy” at 20
Module V
. ⋅ ∼ Ou ou ஆ
Using method of separation of variables, solve 8 =2 7 u, u(x,0)=Se
۷

A tightly stretched string of length / fastened at both ends is initially in a position
given by y = kx, 0 1. Ifit is released from rest from this position, find the

displacement y(x,t) at any time t and any distance x from the end x = 0.
OR
A string is stretched and fastened in two points 50 cm apart. Motion is started by

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