Unformatted text preview: °° + b y ° + c y = 0 , y ( t ) = y , y ° ( t ) = y ° ; is the Function y ( t ) = c 1 e r 1 t + c 2 e r 2 t in terms oF the constants c 1 = y ° − r 2 y r 1 − r 2 e − r 1 t and c 2 = y ° − r 1 y r 2 − r 1 e − r 2 t . § 3.2: Solutions of Linear Homogeneous Equations; the Wronskian. • Consider the initial value problem a ( t ) y °° + b ( t ) y ° + c ( t ) y = f ( t ); y ( t ) = y , y ° ( t ) = y ° . Say that we have an interval I = ² t ∈ R ³ ³ α < t < β ´ such that i. f ( t ) is continuous on I , ii. both b ( t ) and c ( t ) are continuous on I , iii. a ( t ) is continuous yet a ( t ) ° = 0 on I , and iv. t ∈ I . Then there exists a unique solution y = y ( t ) to the initial value problem. This is the Existence and Uniqueness Theorem For linear second order diferential equations. 1...
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 Spring '09
 EdrayGoins
 Equations, Quadratic equation, Elementary algebra, Solutions of Linear Homogeneous Equations

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