Biju Patnaik University of Technology 2007 B.Tech Electronics and Communications Engineering Mathematics 1 - Question Paper
Mathematics Paper one first semester ques. Paper
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general solution cf the differ (b) Write I he tiai equation V + V w,i. the p.** *" in t|le differential equation y y coefficient method. [f the equation y" + P(X)Y + QM 0 series solution about the ordinary point x = a, then write the conditions that P(x) id) |
(g) What is the radius of convergence of the X 2 n l (h) What is the value of P3tl(0), the Legendree polynomial of degree 2n + 1, (i) Write the polynomial expression of P2(x). the Legendree polynomial of degree 2, Find the Laplace transform L(sin(wt)) using the result L(elvVl) - s_lw- |
and Q(X) have to sad sty. WWW.OdiaFilm.COm inn nroblerns
(e) if the equation y" + P(x)y' + Q(*) = 0 has series solution about the regular singular
(a) Find the radius cun/ature of the curve
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point x = a, then write the conditions that P(x) and Q(x) have to satisfy. 0 m (f) Write the solution of the differential equation y' + y - 0 in series, |
a2 b (b) Find the asymptote to the curve y3 = 3ax2. 5 P.TO. |
BSCM 2101
3. Answer the following questions as per the
instruction :
4. Solve the following initial value problems :
(a) y"+ 4y * 4cos{2x) with y(0) = 0 and y' (0) = 2 using method of undetermined coefficient. 5
(b) y"-5y' + 6y = e4* with y(G)andy'(G>-2 using method of variation of parameter.
(a) So/ve the Bernoulli's equation
y'-2xy = 2xy* 5
(b) A tank of 100 gallons capacity is initially full of water. Pure water is allowed to run into the tank at the rate of 1 gallon per minute, and at the same time brine containing 0.25 pounds of salt per gallon flows into the tank at the rate of 1 gallon per minute. If the mixture is allowed to flow out at the rate of 2 gallons per minute after periect mixing, (hen find thqj'i amount of salt in the tank after f minutes.
5. , Answer the following questions according to
(a) Solve the equation (x -1)y"- xy' + y = 0 by reducing the order using y = e* as one of the solution. 5
(b) Solve Cauchy-Euler equation
x2y" - 5xy' + 3y = 0
by reducing into constant coefficient
differential equation.
5
P.T.O.
5
a
a
(X
a t
HU =
(2a -t), 0.
6- Answer according to the instruction ;
aj Find the series solution of the differential equation y"- 9y-0 with y(0)=1 and y'(0) - 0. 5
(b) Prove the identity 5
Answer according to the instruction ,
(aj Find the Laplace transform of the function
0 < t < a
a < t < 2a otherwise
cosfxj.
2 v
nx
t
(b) Find ihe inverse Laplace transform of
F(s> = SS -9)' 5
8. Answer the following questions according to the instruction
4 % (a] Solve the initial value problem y" \ y-2
with y(0) = 0 and y'(0) = 2 using Laplace transform. 5
1
(b) If f 1 9J J then show that
ii
( g = 9 ! f 5 i
dAdd?
-C
BSCM 2101 Contd, BSCM 2101
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| Earning: Approval pending. |
