Unformatted text preview: + 1) + âˆš âˆ† 2 , where the discriminant âˆ† := ( Î» + 1) 2 âˆ’ 4( Î» + 3). We consider two cases: i) If Î» + 3 < 0, i.e. Î» < âˆ’ 3, then âˆ† > ( Î» + 1) 2 and the root r 2 > ( Î» + 1) +  Î» + 1  2 = 0 . Therefore, the solution x ( t ) = e r 2 t is unbounded as t â†’ + âˆž . ii) If Î» + 3 â‰¥ 0, i.e. Î» â‰¥ âˆ’ 3, then âˆ† â‰¤ ( Î» + 1) 2 . If âˆ† < 0, then a fundamental solution set to (5.14) is e ( Î» +1) t/ 2 cos Â³ âˆš âˆ’ âˆ† t 2 Â´ , e ( Î» +1) t/ 2 sin Â³ âˆš âˆ’ âˆ† t 2 Â´ . (5.15) 272...
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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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