Unformatted text preview: [ y c ( t )] 2 holds for all t 6 = c . In particular, at t = 0, y c (0) = − [ y c (0)] 2 . (We assume that c 6 = 0; otherwise, t = 0 is not in the domain.) Obviously, this equality fails for any positive initial velocity y (0), in particular, it is false for given data, y (0) = 1 and y (0) = 2. 6. Rewriting given equation in the equivalent form y = ( − k/m ) y , we see that the function f ( y ) in the energy integral lemma is ( − k/m ) y . So, F ( y ) = Z ± − k m y ² dy = − k 2 m y 2 + C. 228...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Derivative, Elementary algebra, C1 C2

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