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Unformatted text preview: y = 1. The square root is only defned when ( t +2) ( t 2 +2) is nonnegative. The polynomial t 2 +2 is always positive, so we also need t 2. Since we choose the negative square root, the region R is R = ( t, y ) R 2 2 < t < , < y < 1 . Figure 1. Plot o y 2 2 y = t 3 + 2 t 2 + 2 t + 3-4.8-4-3.2-2.4-1.6-0.8 0.8 1.6 2.4 3.2 4 4.8-3.2-2.4-1.6-0.8 0.8 1.6 2.4 3.2 Population Dynamics Autonomous Equations. Recall that a frst order dierential equation is always in the orm dy dt = G ( t, y ) or some unction G ( t, y ). We say that such a dierential equation is an autonomous equation i this unction is a unction o y alone i.e., i G ( t, y ) = f ( y )...
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue University-West Lafayette.
- Spring '09