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Unformatted text preview: This is a third order homogeneous linear diFerential equation with constant coecients. Its auxiliary equation is 3 r 3 + 10 r 2 + 9 r + 2 = 0. actoring yields 3 r 3 + 10 r 2 + 9 r + 2 = (3 r 3 + 3 r 2 ) + (7 r 2 + 7 r ) + (2 r + 2) = (3 r 2 + 7 r + 2)( r + 1) . Thus the roots of the auxiliary equation are r = 1 and r = 7 p 7 2 4(3)(2) 6 = 2 , 1 3 , and a general solution is given by y ( t ) = c 1 e 2 t + c 2 e t + c 3 e t/ 3 . 248...
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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 University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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