Section 3.8 - Notes for Day e Method of Undetermined Coe...

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Unformatted text preview: Notes for Day : § . : e Method of Undetermined Coe cients At the end of class last time, we discussed that if we can nd a “seed” solution (called a particular solution , and notated y P ) for a nonhomogeneous di erential equation, we can generate all the solutions for the di erential equation by combining the seed solution with the general solution to the corresponding homogeneous equation (called the complementary solution , notated y C ). p. , Show that y P ( t ) = ( t + ) is a solution to the di erential equation y ′′- y ′ + y = t , and then form the general solution. Our goal for today is to come up with techniques for nding these “seed” solutions to get us started. e Princip e of Superposition e Principle of Superposition states that (basically) you can work term-by-term to nd the particular solution to a nonhomogeneous equation. Examp e: Form the genera so ution to the di erentia equation y ′′ + y = t + e t ....
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This note was uploaded on 04/05/2008 for the course MATH 2214 taught by Professor Edesturler during the Spring '06 term at Virginia Tech.

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Section 3.8 - Notes for Day e Method of Undetermined Coe...

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