Hello everyone, I'm trying to solve the standard 2nd order differential equation with constant coefficients listed below under the specified boundary conditions:
-dP(x)^2/dx^2 = C * P(x) where C=(2*E*m)/h^2
under the boundary conditions P(-L/2)=0 and P(L/2)=0 for some constant L>0.
Matlab is able to solve the equation with the expected general solution, however, when I apply the boundary conditions, the 'dsolve' command fails. I know a solution exists under these boundary conditions because I can successfully solve the equation by hand, and the solution is listed in a textbook.
Matlab correctly calculates the general solution 'P(x)':
syms C E m h P(x) real C=(E*2*m)/h^2; assume(C>0 & E>0 & m>0 & h>0) P(x)=dsolve( -diff(P,2)==C*P )
However, when I attempt to apply the boundary conditions Matlab calculates P(x)=0. I would appreciate any advice on how to correctly setup Matlab to solve this type of differential equation.
syms C E m h L P(x) real C=(E*2*m)/h^2; assume(C>0 & E>0 & m>0 & h>0 & L>0) P(x)=dsolve( -diff(P,2)==C*P, P(-L/2)==0, P(L/2)==0 )