Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y (x) =c, +c;x +c,¢ +de' cos Be' sinx c) y(x) = Ce¯+ ei(Acosx + Bsinx) +xe %3D d) v(x)-c, +c, x +c,e*' +Ae ' cost + Be' sin x Q.2) The basis of the equation y'' + y" = (0 ,are: a) 1,1.e Q.3) Ihe radius of convergence of (1- x³)y" + 4y' + 6xy = 0 about x, = 0, is: b) 1,1,e- c) 1, x , e d) 1, x, e a)+ o b) 2 c) 0 b) –12e c) be² d) -6e d) 1 Q.4) The Wronskian W(e-2", e', e²*), is: a) 12e Q.5) The general solution of the equation y" + 9y" = 0, is: a) y(x) = c; + c + Acos2x + Bsin2x c) y(x) = c; + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is (arc): a) 12 Q.7) To write the power series E=3 4m as the form E-zum ,we must shift m to become : a) m - 1 Q.8) The characteristic equation for y"'" + 3y" – 4y = 0 , is : a) 2' = 32? Q.9) The form of the particular solution of the equation y" – 9y = 4 sin 3x + 2cos3x , is: a) y,(x) = A cos3x b)y(x) = c; + (2x + Acos2x + Bsin2x d) y(x) = c, + c,x + Acos3x + Bsin3x %3D b) +2i c) 0 d) (0 ,±2i } 3D3 b) m – 2 c) m +1 d) m +2 b) 2 = 32-4 c) d* + 2 = -1 d) 2' = -322 + 4 %3D %3! b) y,(x) = A cos3x + Bsin3x d) y, (x) = Axcos3x + Bxsin3x c) y, (x) = A sin3x Q.10) The recurrence relation which obtained from solving y" + xy = 0 by using power series, is: a) - am-1 = (m + 2)(m + 1)a,m+2 %3D b) am+2 (m +2)(m +1) c) am = (m – 2)(m – 1)a,m+2 d) am+2 = (m+2)(m+ 1) Q.11) Rewrite the series x E-1 m am x™-1 + E-o amx™ as a single power series whose general term involves xm: a) Em=s(am-1 – am-4) x™ c) a, + Em-s(am-1 – am-4) x™ Q.12) The solution of y" + y' = 0 by using power series method , is: b) E(am-1 - am-3) x™ d) a, + Em=:(m am + am) x™ %3! a) y(x) = a, – a,(1-+ b) y(x) = a, + a;(1+- + ...) 2! c) y(x) = a, + a;(x : d)y(x) = a, + a,(x + + 41 + ...) %3D %3D 2! (-1)"x" Q.13) The interval and radius of convergence for power series Em-o° b) (-0, +o), 1 , respectively , are : d) (-m, +), 3 m! c) (-o, +o), 2
Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y (x) =c, +c;x +c,¢ +de' cos Be' sinx c) y(x) = Ce¯+ ei(Acosx + Bsinx) +xe %3D d) v(x)-c, +c, x +c,e*' +Ae ' cost + Be' sin x Q.2) The basis of the equation y'' + y" = (0 ,are: a) 1,1.e Q.3) Ihe radius of convergence of (1- x³)y" + 4y' + 6xy = 0 about x, = 0, is: b) 1,1,e- c) 1, x , e d) 1, x, e a)+ o b) 2 c) 0 b) –12e c) be² d) -6e d) 1 Q.4) The Wronskian W(e-2", e', e²*), is: a) 12e Q.5) The general solution of the equation y" + 9y" = 0, is: a) y(x) = c; + c + Acos2x + Bsin2x c) y(x) = c; + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is (arc): a) 12 Q.7) To write the power series E=3 4m as the form E-zum ,we must shift m to become : a) m - 1 Q.8) The characteristic equation for y"'" + 3y" – 4y = 0 , is : a) 2' = 32? Q.9) The form of the particular solution of the equation y" – 9y = 4 sin 3x + 2cos3x , is: a) y,(x) = A cos3x b)y(x) = c; + (2x + Acos2x + Bsin2x d) y(x) = c, + c,x + Acos3x + Bsin3x %3D b) +2i c) 0 d) (0 ,±2i } 3D3 b) m – 2 c) m +1 d) m +2 b) 2 = 32-4 c) d* + 2 = -1 d) 2' = -322 + 4 %3D %3! b) y,(x) = A cos3x + Bsin3x d) y, (x) = Axcos3x + Bxsin3x c) y, (x) = A sin3x Q.10) The recurrence relation which obtained from solving y" + xy = 0 by using power series, is: a) - am-1 = (m + 2)(m + 1)a,m+2 %3D b) am+2 (m +2)(m +1) c) am = (m – 2)(m – 1)a,m+2 d) am+2 = (m+2)(m+ 1) Q.11) Rewrite the series x E-1 m am x™-1 + E-o amx™ as a single power series whose general term involves xm: a) Em=s(am-1 – am-4) x™ c) a, + Em-s(am-1 – am-4) x™ Q.12) The solution of y" + y' = 0 by using power series method , is: b) E(am-1 - am-3) x™ d) a, + Em=:(m am + am) x™ %3! a) y(x) = a, – a,(1-+ b) y(x) = a, + a;(1+- + ...) 2! c) y(x) = a, + a;(x : d)y(x) = a, + a,(x + + 41 + ...) %3D %3D 2! (-1)"x" Q.13) The interval and radius of convergence for power series Em-o° b) (-0, +o), 1 , respectively , are : d) (-m, +), 3 m! c) (-o, +o), 2
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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