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)
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2.-
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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
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