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Unformatted text preview: r that works, you will need a second solution y 2 ( x ) that is linearly independent of the ±rst. This can be done by the following Method of Reduction of Order: Substitute y 2 ( x ) = y 1 ( x ) u ( x ) into Equation (1), do the di²erentiations and note that several terms cancel out . Now substitute v = u into the resulting equation after the cancelations, and you will obtain a ±rst order equation for v . Solve for v and then integrate to ±nd u ! 1...
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This note was uploaded on 01/06/2012 for the course MATH 4038 taught by Professor Staff during the Summer '08 term at LSU.
 Summer '08
 Staff
 Approximation

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