By Pandey, Rajesh.
Read or Download A Text Book of Engineering Mathematics. Volume II PDF
Similar technique books
IL-2 Sturmovik in motion КНИГИ ;ВОЕННАЯ ИСТОРИЯ Издательство: Squadron/Signal publicationsСерия: airplane 155Автор(ы): Hans-Heiri StapferЯзык: EnglishГод издания: 1995Количество страниц: 49ISBN: 0-89747-341-8Формат: pdf (72 dpi) 1520x1150Размер: 12. 2 mbRapid 17
Considering its advent in 1953, the means of extracorporeal flow has advanced quickly, with advancing know-how resulting in advancements within the simplification of the apparatus concerned. advancements within the knowing and alertness of simple technological know-how have additionally had a big impact as our figuring out of the complicated anatomy, biochemistry, pharmacology and pathophysiology of the center keep growing.
- 15900 HVAC Instrumentation and Controls
- Formulation Engineering of Foods
- Triumph Bonneville, T100, Speedmaster, America, Thruxton and Scrambler Service and Repair Manual - 2001 to 2007 (Haynes Service and Repair Manuals)
- Orchard Introduction to Simulink with Engineering Applications
- Molybdenum Disulphide Lubrication (Tribology and Interface Engineering) (Tribology and Interface Engineering)
Extra info for A Text Book of Engineering Mathematics. Volume II
2oo1) (a) x2 + y2 - 2xy = C (b) . (c) X2 + 4xy + y2 = C (d) xy+y2+ x2 = C xy + y2 - x2 = C Ans. (d) 10. In the differential equation x dy + my = e- x , if the integrating factor is -\-' dx x then the value of m is (a) 2 (b) -2 (c) 1 (d) -1 35 A Textbook of Engineering Mathematics Volume - II Ans. (b) 11. S. 1988) (b) log (y2 -1) (d) none of these = Clog (X2 + 1) _x2 e (c) y2= 1 + C 2 x Ans. (c) 12. S. S. S. 1995) 1 (a) eY = ex + - x3 + C 3 (b) (c) eY = ex + x3 + C (d) 1 eY = e-X+ - x3 + C 3 Ans.
F(a) is constant e ax f(D) e ax = _1_ f(a) eax if f(a) "# 0 , Case II. I. I. = - - e ax f (D) = eax x2 - - if f" (a) "# 0 f" (a)' Example 1. Solve (D2 - 2D + 5) Y = e- X 42 Linear Differential Equations with Constant Coefficients and Applications Solution. Here auxiliary equation is m 2 - 2m + 5 = 0, whose roots are m=-1±2i :. CP. = e- X [Cl cos 2x + C2 sin 2x], where Cl and C2 are arbitrary constants and P.. : here a =-1 1 -x =-e 8 :. The required solution is y = CP. I. e. y = e- X(Cl cos 2x + C2 sin 2x) + ?
Solve dy + 2y tan x = sin x, given that y = 0 when x = rt/3. S. 2003) Solution. Here P = 2 tan x and Q = sin x ... Integrating factor = e lpdx = e l2tan xdx = e210g sec x Multiplying the given equation by sec2x, we get 2 sec x (~~ 2 + 2y tan x) = sin x sec x d or ' - (y sec 2x) = sec x tan x dx Integrating both sides with respect to x, we get J sec x tan x dx, y sec2 x = C + ysec 2 x=C+secx or it is given that when x = rtj3, y ... from (1) 0 where C is an arbitrary constant x = (1) 0 2 rt rt sec - = C + sec 3 3 17 A Textbook of Engineering Mathematics Volume - II or 7t 0=C+2 :.