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Q.3) The radius of convergence of (1- x²)y" + 4y' + 6xy = 0 about xo = 0 , is: d) 1 %3D b) 2 c) 0 2x

Q.3) The radius of convergence of (1- x²)y" + 4y' + 6xy = 0 about xo = 0 , is: d) 1 %3D b) 2 c) 0 2x

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q.1) The general solution of the equation y* • v• ' -e' cos x , ÁN: a) y(x ) =c, +c; x +c,¢ ' Ae' cosa a Re' sin x b) y (x ) =c, +c,x +c,¢ + de' cos a + Be' sinx c) y(x) = Ce¯' + ei(Acosx + Bsinx) + xe d) v (x ) -c, +c, x +c,e¨ +Ae ' cosx + 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- x²)y" + 4y' + 6xy = 0 about xo = 0 , is: b) 1 , 1, e¯' c) 1,x,e² d) 1 , x , e" %3D a)+ o b) 2 c) 0 b) - 12e?* с) бе? d) 1 d) -6e" Q.4) The Wronskian W(e~2", e", e²*), is: Q.5) The general solution of the equation y" + 9y" = 0 , is: a) y(x) = c; + cz + Acos2x + Bsin2x c) y(x) = c; + c; + 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 Em=3 4m as the form £-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 c) y, (x) = A sin3x Q.10) The recurrence relation which obtained from solving y" + xy = 0 by using power series , is: a) 12e* b)y(x) = c, + c,x + Acos2x + Bsin2x d) y(x) = c, + c,x + Acos3x + Bsin3x b) ±2i c) 0 d) (0 , ±2i } b) т - 2 с) т +1 d) m +2 b) 23 = 322-4 c) d* + 2 = -1 d) 2' = -32? + 4 %3D b) y,(x) = A cos3x + Bsin3x d) y, (x) = Axcos3x + Bxsin3x a) – am-1 = (m + 2)(m + 1)a,m+2 b) am+2 %3D (m +2)(m+1) с) а, 3D (т — 2)(m - 1)а,m+2 d) am+2 (m+2)(m+ 1) Q.11) Rewrite the series x E=1m am x™-1 + £m-0 amx™ as a single power series whose general term involves xm: a) E=s(am-1 – am-4) x™ c) a, + Em-5(am-1- am-4) x™ Q.12) The solution of y" + y' = 0 by using power series method , is: b) E-4(am-1 – am-3) x™ d) a, + Em=1(m am + am) x™ Am-4) xm a) y(x) = ao – a;(1 – b) y(x) = a, + a(1+ 2! 3! x* с) у (x) %3D а, + а,(х-: d)y(x) = ao + a,( x + + ..) + 5! 2! 4! (-1)™x" Q.13) The interval and radius of convergence for power series Em-o b) (-∞, +m), 1 , respectively , are : d) (-m, +∞), 3 m! a) (-∞, +∞), ∞ c) (-∞, +∞), 2
Transcribed Image Text:Q.1) The general solution of the equation y* • v• ' -e' cos x , ÁN: a) y(x ) =c, +c; x +c,¢ ' Ae' cosa a Re' sin x b) y (x ) =c, +c,x +c,¢ + de' cos a + Be' sinx c) y(x) = Ce¯' + ei(Acosx + Bsinx) + xe d) v (x ) -c, +c, x +c,e¨ +Ae ' cosx + 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- x²)y" + 4y' + 6xy = 0 about xo = 0 , is: b) 1 , 1, e¯' c) 1,x,e² d) 1 , x , e" %3D a)+ o b) 2 c) 0 b) - 12e?* с) бе? d) 1 d) -6e" Q.4) The Wronskian W(e~2", e", e²*), is: Q.5) The general solution of the equation y" + 9y" = 0 , is: a) y(x) = c; + cz + Acos2x + Bsin2x c) y(x) = c; + c; + 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 Em=3 4m as the form £-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 c) y, (x) = A sin3x Q.10) The recurrence relation which obtained from solving y" + xy = 0 by using power series , is: a) 12e* b)y(x) = c, + c,x + Acos2x + Bsin2x d) y(x) = c, + c,x + Acos3x + Bsin3x b) ±2i c) 0 d) (0 , ±2i } b) т - 2 с) т +1 d) m +2 b) 23 = 322-4 c) d* + 2 = -1 d) 2' = -32? + 4 %3D b) y,(x) = A cos3x + Bsin3x d) y, (x) = Axcos3x + Bxsin3x a) – am-1 = (m + 2)(m + 1)a,m+2 b) am+2 %3D (m +2)(m+1) с) а, 3D (т — 2)(m - 1)а,m+2 d) am+2 (m+2)(m+ 1) Q.11) Rewrite the series x E=1m am x™-1 + £m-0 amx™ as a single power series whose general term involves xm: a) E=s(am-1 – am-4) x™ c) a, + Em-5(am-1- am-4) x™ Q.12) The solution of y" + y' = 0 by using power series method , is: b) E-4(am-1 – am-3) x™ d) a, + Em=1(m am + am) x™ Am-4) xm a) y(x) = ao – a;(1 – b) y(x) = a, + a(1+ 2! 3! x* с) у (x) %3D а, + а,(х-: d)y(x) = ao + a,( x + + ..) + 5! 2! 4! (-1)™x" Q.13) The interval and radius of convergence for power series Em-o b) (-∞, +m), 1 , respectively , are : d) (-m, +∞), 3 m! a) (-∞, +∞), ∞ c) (-∞, +∞), 2
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