Unformatted text preview: u xu 1 2 ' ' + = 2 2 2 1 2 2 u xu u ' ' ' + + = u xu 1 2 ' ' = 2 2 2 2 2 2 ( ' ) ' '+ + = xu xu u u x 1 2 ' = u 2 2 ' = Integrate to find u 1 and u 2 u x dx x 1 2 2 = = ∫ u dx x 2 2 2 = = ∫ Using the formula for a particular solution y x u y u y p ( ) = + 1 1 2 2 we have y x x e x xe p x x ( ) ( ) = + 2 2 2 2 which simplifies to the expression y x x e p x ( ) = 2 2 We then append this term to the general solution for the associated homogeneous equation to obtain the general solution y c e c xe x e c x x x = + + 1 2 2 2 2 2 If initial values are given, they can be applied to this solution and its derivative....
View
Full Document
 Spring '08
 comech
 Equations, u2, associated homogeneous equation

Click to edit the document details