GTU BE/B.Tech 2019 Winter Question Papers || Gujarat Technological University
Subject Code: MTH0002
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE - SEMESTER- I & II (SPFU) EXAMINATION - WINTER 2019
Subject Name: Ordinary Differential Equation
Time: 10:30 AM TO 01:00 PM
Instructions:
- Attempt any five questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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| Q.1 | (a) | Check whether the given differential equation is exact or not (x2 + y2)dx—(2x2y —4xy3 +sin y)dy = 0 .Hence find the general solution. | 03 |
| (b) | Find the orthogonal trajectories of the family of semi cubical parabolas ay2 = x3 | 04 | |
| Q.2 | (a) | Solve y'' -3y' + 2y = ex by using variation of Parameter method | 07 |
| (b) | Find the Wronskian of y1,y2 of y''-2y'+y =exlogx | 03 | |
| Q.3 | (a) | Solve y'' + y = cosx cosx+sinx = ex | 04 |
| (b) | Using Method of undetermined Coefficient solve y''+ 4y = 8x2 | 07 | |
| Q.4 | (a) | Find the orthogonal trajectories of cardioid r = a(1 - cos ?) | 07 |
| (b) | Find the Series solution of y'-2xy =0 | 07 | |
| Q.5 | (a) | Solve x2y"—xy'+ y=x | 07 |
| (b) | Discuss about Singular point and classify singular pints for the differential equation x2 (x-1)y"+3(x-1)y'+7xy=0 | 07 | |
| Q.6 | (a) | Solve in Series the differential equation 4x2y'' + 1/xy' - y +y=0 | 07 |
| (b) | The population of a country increases at the proportional to the current population. if the population doubles in 40 years, in how many years will it triple itself. | 07 | |
| Q.7 | (a) | Solve (x2y2 +2)ydx +(2-x2y)xdy =0 | 07 |
| (b) | Solve (D2 —1)y =xex where D = d/dx | 07 | |
| (a) | Solve the initial value Problem y"-9y =0,y(0) =2, y'(0)=-1 | 07 | |
| (b) | If y1 =x is one solution of x2 y"+xy'—-y =0.Find the second solution | 07 |
Date: 07/01/2020
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Total Marks: 70
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