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Unformatted text preview: y is now odd rather than even. Determine the qualitative behavior of the solution graphically. Then ±nd the solution and explain its behavior. (c) Explain why the behavior now depends on whether n is even or odd without referring to the exact solution. 3. Consider the two equations y = y + 1 , y (0) = 1 , (2) and z = z + 1 , z (5) = 1 . (3) Note that the solutions y ( t ) and z ( t ) satisfy the same equation. Only the initial condition differs. Without ±nding the solution show that z ( t ) = y ( t-5) . 4. Suppose we now consider the two equations y = y + t, y (0) = 1 , (4) and z = z + t, z (5) = 1 . (5) Can you still say that z ( t ) = y ( t-5) ?...
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- Fall '08
- equation dy, -1. dt Note