Problemas de Condiciones de contorno En estos ejercicios interesa definir un cambio en la variable dependiente de la forma y(x) = z(x) + m(x) de modo que en la nueva ecuación diferencial la variable dependiente sea z(x) y tenga condiciones de contorno homogéneas. En todos los casos la ecuación diferencial tiene la forma: p( x ) ⋅ y ′′ + q( x ) ⋅ y ′ + r( x ) ⋅ y = f ( x ) . Se desea obtener m(x) y la forma de la nueva ecuación diferencial con la variable z(x) 1.- 2.- 3.- 4.- 5.- 6.- 7.- 8.- 9.- 10.- 11.- 12.- 5 ⋅ y(0) = 14 y(1) = 12 5 ⋅ y(0) = 14 y ′(1) = 12 5 ⋅ y(0) + 8 ⋅ y ′(0) = 14 y ′(1) = 12 5 ⋅ y(0) + 8 ⋅ y ′(0) + 5 ⋅ y(1) = 14 25 ⋅ y(1) + 6 ⋅ y ′(1) = 12 5 ⋅ y(0) + 8 ⋅ y ′(0) + 5 ⋅ y(1) + 8 ⋅ y ′(1) = 14 3 ⋅ y(1) − 8 ⋅ y ′(1) = 12 5 ⋅ y(0) + 8 ⋅ y ′(0) + 5 ⋅ y(1) + 8 ⋅ y ′(1) = 14 6 ⋅ y(0) + 5 ⋅ y(1) + 6 ⋅ y ′(1) = 12 5 ⋅ y(0) + 8 ⋅ y ′(0) + 5 ⋅ y(1) + 8 ⋅ y ′(1) = 14 6 ⋅ y(0) − 8 ⋅ y ′(0) + 15 ⋅ y(1) + 6 ⋅ y ′(1) = 12 8 ⋅ y ′(0) + 5 ⋅ y(1) + 8 ⋅ y ′(1) = 14 6 ⋅ y(0) − 8 ⋅ y ′(0) + 15 ⋅ y(1) + 6 ⋅ y ′(1) = 13 8 ⋅ y ′(0) + 5 ⋅ y(1) = 14 13 ⋅ y ′(0) + 15 ⋅ y(0) + 6 ⋅ y ′(1) = 12 5 ⋅ y(0) − y(1) = 14 4 ⋅ y(0) − 8 ⋅ y ′(0) + 15 ⋅ y(1) + 6 ⋅ y ′(1) = 12 y(0) + 8 ⋅ y ′(1) = 14 6 ⋅ y(0) − 8 ⋅ y ′(0) + 15 ⋅ y(1) + 6 ⋅ y ′(1) = 12 5 ⋅ y(0) + 8 ⋅ y ′(0) = 1 15 ⋅ y(1) + 6 ⋅ y ′(1) = 2 ______________________________ Copyright © 2007 by Tecnun (University of Navarra) 1/1