part - + a 1 t + a ] cos βt t r [( A n t n + · · · A 1...

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Form of Particular Solution (Adapted from Table 3.1 of Kohler and Johnson) The right-hand column gives the proper form to assume for a particular solution of ay ′′ + by + cy = g ( t ). In the right-hand column, choose r to be the smallest nonegative integer such that no term in the assumed form is a solution of the homogeneous equation ay ′′ + by + cy = 0. The value of r will be 0, 1, or 2. Form of g ( t ) Form to Assume for a Particular Solution y p ( t ). a n t n + · · · + a 1 t + a 0 t r [ A n t n + · · · A 1 t + A 0 ] [ a n t n + · · · + a 1 t + a 0 ] e αt t r [ A n t n + · · · A 1 t + A 0 ] e αt [ a n t n + · · · + a 1 t + a 0 ] sin βt or [ a n t n + · · ·
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Unformatted text preview: + a 1 t + a ] cos βt t r [( A n t n + · · · A 1 t + A ) sin( βt ) + ( B n t n + · · · B 1 t + B ) cos( βt )] e αt sin( βt ) or e αt cos( βt ) t r b Ae αt sin( βt ) + Be αt cos( βt ) B e αt [ a n t n + · · · + a ] sin βt or e αt [ a n t n + · · · + a ] cos βt t r [( A n t n + · · · + A ) e αt sin( βt ) + ( B n t n + · · · + B ) e αt cos( βt )]...
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This note was uploaded on 11/11/2009 for the course MATH 3200 taught by Professor Bennethum during the Spring '06 term at University of Colombo.

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