Unformatted text preview: has the Form y ( t ) = c 1 e − 3 t + c 2 e t/ 2 + c 3 te t/ 2 . 21. ±irst, we solve the corresponding homogeneous equation, y − 3 y + 7 y = 0 . Since the roots oF the auxiliary equation, r 2 − 3 r + 7 = 0, are r = 3 ± √ 9 − 28 2 = 3 ± √ 19 i 2 , a general solution to the homogeneous equation is y h ( t ) = c 1 cos √ 19 t 2 + c 2 sin √ 19 t 2 e 3 t/ 2 . 249...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Prime number, general solution, auxiliary equation

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