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Convert the given second-order equation into a system by setting v=y'. Then find all the critical points in the yv-plane. Finally, sketch the direction field and describe the stability of the critical points. d²y dt² વા -3y=-3 Find all the critical points in the yv-plane. (y.v) = (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) Sketch the direction field. Choose the correct graph below. O A. OB. O C. V -3-2-1 0 1 2 3 5 -3-2-1 0 1 2 3 y Describe the stability of the critical points. Which critical points correspond to an asymptotically stable node? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (y.v) = (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) OB. There are no critical points that correspond to an asymptotically stable node. Which critical points correspond to an unstable node? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. -3-2-1 0 1 2 3 y O A. The critical point(s) is/are (y.v)=. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an unstable node. Which critical points correspond to an asymptotically stable spiral? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) OB. There are no critical points that correspond to an asymptotically stable spiral. O D. -3-2-1 0 1 2 3 y

Convert the given second-order equation into a system by setting v=y'. Then find all the critical points in the yv-plane. Finally, sketch the direction field and describe the stability of the critical points. d²y dt² વા -3y=-3 Find all the critical points in the yv-plane. (y.v) = (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) Sketch the direction field. Choose the correct graph below. O A. OB. O C. V -3-2-1 0 1 2 3 5 -3-2-1 0 1 2 3 y Describe the stability of the critical points. Which critical points correspond to an asymptotically stable node? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (y.v) = (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) OB. There are no critical points that correspond to an asymptotically stable node. Which critical points correspond to an unstable node? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. -3-2-1 0 1 2 3 y O A. The critical point(s) is/are (y.v)=. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an unstable node. Which critical points correspond to an asymptotically stable spiral? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) OB. There are no critical points that correspond to an asymptotically stable spiral. O D. -3-2-1 0 1 2 3 y

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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Convert the given second-order equation into a system by setting v=y'. Then find all the critical points in the yv-plane. Finally, sketch the direction field and describe the stability of the critical points. d²y dt² - 3y = - 3 Find all the critical points in the yv-plane. (y.v) = (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) Sketch the direction field. Choose the correct graph below. O A. V 3 -3-2-1 0 1 2 3 y O B. V WN YY YYY YYY **** **** -3-2-1 0 1 2 3 y ← O C. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an asymptotically stable spiral. -3-2-1 0 1 2 3 y Describe the stability of the critical points. Which critical points correspond to an asymptotically stable node? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an asymptotically stable node. Which critical points correspond to an unstable node? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v)=- (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an unstable node. Which critical points correspond to an asymptotically stable spiral? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O D. -3-2-1 0 1 2 3 y
Transcribed Image Text:Convert the given second-order equation into a system by setting v=y'. Then find all the critical points in the yv-plane. Finally, sketch the direction field and describe the stability of the critical points. d²y dt² - 3y = - 3 Find all the critical points in the yv-plane. (y.v) = (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) Sketch the direction field. Choose the correct graph below. O A. V 3 -3-2-1 0 1 2 3 y O B. V WN YY YYY YYY **** **** -3-2-1 0 1 2 3 y ← O C. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an asymptotically stable spiral. -3-2-1 0 1 2 3 y Describe the stability of the critical points. Which critical points correspond to an asymptotically stable node? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an asymptotically stable node. Which critical points correspond to an unstable node? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v)=- (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an unstable node. Which critical points correspond to an asymptotically stable spiral? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O D. -3-2-1 0 1 2 3 y
Which critical points correspond to an unstable spiral? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an unstable spiral. Which critical points correspond to a saddle point? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to a saddle point. Which critical points correspond to a center point? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to a center point.
Transcribed Image Text:Which critical points correspond to an unstable spiral? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to an unstable spiral. Which critical points correspond to a saddle point? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to a saddle point. Which critical points correspond to a center point? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) is/are (y.v) =. (Simplify your answer. Use a comma to separate answers as needed. Type an ordered pair.) O B. There are no critical points that correspond to a center point.
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