JaimePerezAparicioEjercicioPropuestoenclase18122012

math u_{xx} + \frac{2}{x} u_x = l^2 f(x) math

Con el cambio de variable: math u=Cerf(x)=\frac{2C}{\pi} \int_{0}^{x} e^{-t^2} dt math

donde: math \frac{\partial u}{\partial x} = \frac{2C}{\sqrt{\pi}} \frac{\partial}{\partial x} \int_{0}^{x} e^{-t^2} dt = \frac{4C}{\pi} e^{-x^2} math

y: math \frac{\partial ^2 u}{\partial x^2}= \frac{-8Cx}{\pi} e^{-x^2} math

queda: math f(x)=\frac{8C}{\pi l^2} \frac{1-x^2}{x} e^{-x^2} math