Unformatted text preview: . Using the quadratic formula, we ±nd that the other two roots are r = 2 ± √ 4 − 12 2 = 1 ± √ 2 i. A general solution is, therefore, y ( t ) = c 1 e − t + c 2 e t cos √ 2 t + c 3 e t sin √ 2 t . (b) By inspection, r = 2 is a root of the auxiliary equation, r 3 + 2 r 2 + 5 r − 26 = 0. Since r 3 + 2 r 2 + 5 r − 26 = ( r − 2) ( r 2 + 4 r + 13 ) , the other two roots are the roots of r 2 + 4 r + 13 = 0, that is, r = − 2 ± 3 i . Therefore, a general solution to the given equation is y ( t ) = c 1 e 2 t + c 2 e − 2 t cos 3 t + c 3 e − 2 t sin 3 t . 182...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Quadratic equation, auxiliary equation, possible rational roots

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