This is what I expected!! I really appreciate your help with my problem! Thank you so much!!
Thank you very much for helping me! But I still exist two problems:
Could I eliminate constant C by the second condition? how can i do that?
Please help me one more!! I sincerely thank you very much!
For a linear DE with linear BCs, there is always an arbitrary multiplicative constant in the solution. The constant is often determined by a normalization condition on f(x).
Well, if C[1] is not equal zero, then the solution will diverge. So if you want the limit to be finite, i.e. $<\infty$, then the only thing that works is C[1]=0. So using that condition of yours, the only choice for the constant that works seems to be C[1]=0.
Cheers,
M.
Syntax errors. Try following:
In[1]:= DSolve[{y''[x] == k^2 y[x], y'[0] - h y[0] == 0}, y[x], x]
Out[1]= {{y[x] -> ( E^(-k x) (-h + E^(2 k x) h + k + E^(2 k x) k) C[1])/(h + k)}}
Clearly then Lim x->Infinity, gives y[x]->Infinity
Unless C[1]=0, in which case the solution is constant zero, which appears to be a valid solution.
