Unformatted text preview: + 3 ) . ThereFore, the other two roots oF the auxiliary equation are r = 2 ± √ 4 − 12 2 = 1 ± √ 2 i , and a general solution to the given di±erential equation is given by y ( t ) = c 1 e 2 t + c 2 e t cos √ 2 t + c 3 e t sin √ 2 t . Next, we fnd the derivatives, y ( t ) = 2 c 1 e 2 t + c 2 e t ± cos √ 2 t − √ 2 sin √ 2 t ² + c 3 e t ± sin √ 2 t + √ 2 cos √ 2 t ² , y ( t ) = 4 c 1 e 2 t + c 2 e t ± − cos √ 2 t − 2 √ 2 sin √ 2 t ² + c 3 e t ± − sin √ 2 t + 2 √ 2 cos √ 2 t ² , 181...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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