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Unformatted text preview: t → ∞ ? EXAMPLE. Solve the initial value problem y 002 y3 y = 0, y (0) = α , y (0) = 3. Then ﬁnd α so that the solution approaches 0 as t → ∞ . What happens if we are just a tiny tiny bit oﬀ when we start this system, that is, we start not with y (0) = α but with y (0) = α + ± ? Assume we continue to hit the desired y (0) on the nose. What if we get a repeated root? How do we know we have all the solutions? What if the roots are complex numbers? HOMEWORK: SECTION 3.1...
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 Spring '08
 Fonken
 Differential Equations, Equations, Order Linear ODE

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