Download GTU BE/B.Tech 2019 Winter 3rd Sem Old 130002 Advanced Engineering Mathematics Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER-III (Old) EXAMINATION — WINTER 2019

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Subject Code: 130002

Subject Name: Advanced Engineering Mathematics

Time: 02:30 PM TO 05:30 PM

Date: 22/11/2019

Total Marks: 70

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Instructions:

1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1

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(a) (i) Solve ye^xdx + (2y+e^x)dy =0

(ii) Solve (x + 1)² dy/dx —y = 3 (x + 1)²

(b) Obtain Fourier series of f(x) = x² in the interval(0, 4).

Q.2

(a) (1) Use method of Undetermined coefficients and find general solution of y" + 10y’ + 25y = e^-5x

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(b) Find general solution of (D² + 2D — 35)y = 37 sin 5x

OR

(b) Solve by Variation of parameter method (D² + 9)y = tan3x

Q.3

(a) Find Fourier series of f(x) =e^ax in (0,2p), a >0

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(b) Find Fourier series of f(x) = { X , 0 < x < 2; 4-x, 2 < x < 4 }

OR

(a) Find the Series solution of y"' — 2y’ = 0

(b) Express the function f(x) = { sinx, 0 < x < p; 0, p < x } as a Fourier sine integral and show that ?₀⁸ sin?xsinp? d? = p/2 sinx

Q.4

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(a) (1) Find Laplace transform of e^t(1 + vt)²

(ii) Find the inverse Laplace transform of (2s+2) / (s²+2s+10)

(b) State Convolution theorem and using it find inverse Laplace transform of 1/((s—2)(s+2)²)

OR

(a) (i) Find Laplace transform of e^-3t u(t — 2)

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(1) Find inverse Laplace transform of e^-2s/(s+2)²

(b) Solve initial value problem using Laplace transform method y"' -3y' +2y=12e^-x, y(0)=2,y'(0)=6

Q.5

(a) (1) Form Partial differential equation for the equation z=ax+by+ct

(ii) Find Laplace transform of f(t) = { cost , 0 < t < 2p; 0, t > 2p }

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OR

(a) Find the Series solution of 4xy"" + 2y"' +y =0

(b) Using method of Separation of variables solve ?u/?x =4 ?u/?y given that u(0,y) =8e^-3y

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