Unformatted text preview: y ( t ), we set y ( t ) = − r 7 3 e − 2 t sin ± 2 √ 3 t + φ ² + √ 7 e − 2 t cos ± 2 √ 3 t + φ ² = 0 ⇒ sin ( 2 √ 3 t + φ ) cos ( 2 √ 3 t + φ ) = √ 7 p 7 / 3 = √ 3 ⇒ tan ± 2 √ 3 t + φ ² = √ 3 . Since tan θ = √ 3 when θ = ( π/ 3)+ nπ , where n is an integer, we see that the relative extrema will occur at the points t n , where 2 √ 3 t n + φ = π 3 + nπ ⇒ t n = ( π/ 3) + nπ − φ 2 √ 3 . 239...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Critical Point, Sin, Fermat's theorem, ﬁrst point

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