next up previous
Next: Up: The Method of Separation Previous: The Method of Separation

$C=0$

In this case, the equations (2.24) and (2.25) become

\begin{displaymath}
X^{\prime\prime} = 0, \qquad \Rightarrow \qquad X(x) = A x + B,
\end{displaymath}

and

\begin{displaymath}
\ddot{T} = 0, \qquad \Rightarrow \qquad T(t) = D t + E,
\end{displaymath}

for constants $A$, $B$, $D$ and $E$. However, the boundary conditions (2.17) imply that

\begin{displaymath}
A = 0 \qquad \hbox{and} \qquad B = 0.
\end{displaymath}

Thus, the only solution, with $C=0$, it is trivial solution.

Prof. Alan Hood
2000-10-30