In Problems 19-24, convert the given second-order equation into a first-order system by setting υ = y ′ . Then find all the critical points in the y υ -plane. Finally, sketch (by hand or software) the direction fields, and describe the stability of the critical points (i.e., compare with Figure 5.12 ). y ″ ( t ) + y ( t ) − y ( t ) 3 = 0
In Problems 19-24, convert the given second-order equation into a first-order system by setting υ = y ′ . Then find all the critical points in the y υ -plane. Finally, sketch (by hand or software) the direction fields, and describe the stability of the critical points (i.e., compare with Figure 5.12 ). y ″ ( t ) + y ( t ) − y ( t ) 3 = 0
In Problems 19-24, convert the given second-order equation into a first-order system by setting
υ
=
y
′
. Then find all the critical points in the
y
υ
-plane. Finally, sketch (by hand or software) the direction fields, and describe the stability of the critical points (i.e., compare with Figure 5.12).
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