Differential Equations Lecture Work Solutions 277

Differential Equations Lecture Work Solutions 277 - ) = 1 2...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
2. u ( x, t )= F ( x 2 t )+ G ( x +2 t ) u ( x, 0) = cos x u t ( x, t )=0 u ( x, 0) = F ( x )+ G ( x )=co s x (*) u t ( x, t )= 2 F 0 ( x 2 t )+2 G 0 ( x +2 t ) u t ( x, 0) = 2 F 0 ( x )+2 G 0 ( x )=0 Integrate ⇒− F ( x )+ G ( x )=con s tan t= k (#) solve the 2 equations (*) and (#) 2 G ( x )=co s x + k G ( x )= 1 2 cos x + 1 2 k 2 F ( x )=co s x k F ( x )= 1 2 cos x 1 2 k We need F ( x 2 t ) F ( x 2 t )= 1 2 cos ( x 2 t ) 1 2
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) = 1 2 cos ( x + 2 t ) + 1 2 k u ( x, t ) = 1 2 cos ( x 2 t ) + 1 2 cos ( x + 2 t ) 1 2 k + 1 2 k u ( x, t ) = 1 2 { cos ( x 2 t ) + cos ( x + 2 t ) } 277...
View Full Document

Ask a homework question - tutors are online