Download GTU B.Tech 2020 Summer 3rd Sem 2130002 Advanced Engineerng Mathematics Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER- III EXAMINATION - SUMMER 2020

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Subject Code: 2130002 Date: 26/10/2020

Subject Name: Advanced Engineering Mathematics

Time: 02:30 PM TO 05:00 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) Solve dy/dx = x² + 3x + 2. 03

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(b) Solve dy/dx + 2xy = 2e^-x2. 04

(c) State convolution theorem and use it to find L^-1[1/(s² + a²)]. 07

Q.2 (a) Solve y'' - 3y' + 2y = e^x. 03

(b) Find Fourier series for f(x) = x²; -p < x < p. 04

(c) Find a power series solution of y'' + y = 0 near the ordinary point x=0. 07

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OR

(c) Find Fourier series in the interval (0,2p) if 07

f(x)= { -p 0<x<p
x-p p<x<2p }

and hence show that ? [1/(2n+1)²] = p²/8.

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Q.3 (a) Find L^-1[1/s]. 03

(b) Solve y''' - 4y' - 12y = sinx by method of undetermined coefficient. 04

(c) Solve y'' + y = secx by using method of variation of parameters. 07

OR

Q.3 (a) Solve (d²y/dx²) - 3(dy/dx) + 2y = 0. 03

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(b) Solve (D² - D - 2)y = sin2x. 04

(c) Solve by Charpit’s method p = (z + qy). 07

Q.4 (a) Find L[e^tsin²t]. 03

(b) Find L^-1[1/(s²+6s+18)]. 04

(c) Solve y'' - y' - 2y = 0; with y(0)=1, y'(0)=0 by using Laplace transform. 07

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OR

Q.4 (a) Solve (x² + y²)dx - xy dy = 0. 03

(b) Find cosine series for f(x) = e^x in 0 < x < L. 04

(c) Find Fourier series for f(x) = 3x(p² - x²) in -p < x < p. 07

Q.5 (a) Solve pq = 1. 03

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(b) Solve p² - x = q² - y. 04

(c) Find a series solution of y'' + xy' + y = 0 near the ordinary point x=0. 07

OR

Q.5 (a) Solve ?z/?x = sinxsiny given that z = -2siny when x=0 and z = 0 when y is an odd multiple of p/2. 03

(b) Solve r - 2s + t = sin(2x+3y). 04

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(c) Solve (p² + q²)x = pz. 07

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