Quiz4Asolutions

# Quiz4Asolutions - e-3 t 0 as t . y will tend to zero if we...

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MATH 415.01 QUIZ 4A Feb 3, 2010 SHOW ALL YOUR WORK! GOOD LUCK! NAME: 1. (6.5 pts.) In the following diﬀerential equation, determine the values of α , if any, for which all solutions tend to zero as t → ∞ . y 00 + (4 - α ) y 0 - 3( α - 1) y = 0 r 2 + (4 - α ) r - 3( α - 1) = 0 .i.e. ( r + 3)( r - ( α - 1)) = 0. Thus, r 1 = - 3 , r 2 = ( α - 1). General Solution is y = c 1 e - 3 t + c 2 e ( α - 1) t Obviously,
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Unformatted text preview: e-3 t 0 as t . y will tend to zero if we also have e ( -1) t 0. This is true if ( -1) < 0. i.e. < 1 2. (6 pts.) Find the Wronskian of 2 x and xe x . W = 2 x xe x 2 e x + xe x = 2 x ( e x + xe x )-2 xe x = 2 x 2 e x...
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## This note was uploaded on 07/26/2011 for the course MATH 415 taught by Professor Costin during the Spring '07 term at Ohio State.

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