Download GTU BE/B.Tech 2019 Winter 3rd Sem New 2130002 Advanced Engineering Mathematics Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- III (New) EXAMINATION — WINTER 2019

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Subject Code: 2130002 Date: 22/11/2019
Subject Name: Advanced Engineering Mathematics
Time: 02:30 PM TO 05:30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

MARKS

Q.1 (a) Determine the singular points of the differential equation 03
x(x+1)² y"+(2x-1)y'+ x² y=0 and classify them as regular or irregular.

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(b) (i) Compute ?(%,%) 0
(ii) Define (1) Error Function (2) Beta Function 02

(c) (1) Solve the I.V.P: y"-4y'+4y=0, y(0)=3 & y'(0)=1 03

Q.2 (a) Solve (1+x)ydx + (1-y)xdy = 0 03

(b) Solve (D²-5D+6)y=sin3x 04

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(c) State the convolution theorem and apply it to evaluate L^-1 {?} 07

OR

(c) Using Laplace Transformation, Solve y"+ 6y=1, y(0)=2, y'(0)=0 07

Q.3 (a) Find the Laplace transform of f(t) = { 0, 0<t<2 03
3, t>2

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(b) Find the power series solution of y' =2xy. 04

(c) Obtain Fourier series of the Function f(x)= { 0,-2<x<0 07
1,0<x<2

OR

Q.3 (a) Find the Inverse Laplace Transform of 6/(s²+4) 03

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(b) Find the series solution of y"+x²y=0 in power of x. 04

(c) Obtain Fourier series of the Function f(x)=x+|x|,-p<x<p 07

Q.4 (a) Solve dy/dx + y tanx =sin2x 03

(b) Find a sine series for f(x)=e^x in 0<x<p. 04

(c) By the Method of Separation of variables , solve ?²u/?x² = ?u/?t + u where u(x,0)= 4p 07

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OR

Q.4 (a) Solve ye^xdx+(2y+e^x)dy=0, y(0)=-1 03

(c) Using Undetermined co-efficient method , solve the differential equation Y"+y'—6y = 6x+3x²—6x³ 07

Q.5 (a) Solve z = px+qy+p²q² 03

(b) Find (1) L{e^tcosudu} (2)L^-1{ (2s+2)/(s²+2s+10) } 04

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(c) Find the general solution of P.D.E: (x² —yz) p+ (y² —zx)q=z² —xy 07

OR

Q.5 (a) Form a Partial differential equation from f(xy +z²,x+y+z)=0 03

(b) Find (1) L{?₀^tsinau du} (2) L^-1{ 1/(s⁴+4s²+8) } 04

(c) Using Method of Variation of parameters, Solve (D²-2D+1)y =3x²e^x 07

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