表2‐2边界条件为下列表格所示,微分方程为:222()()0dXxXxdx0xL时的解(,)mXx、范数()mN和特征值m序号x=0处的边界条件x=L处的边界条件(,)mXx1/()mNm是下面方程的正根110dXHXdx20dXHXdxcossin1xmmHxm222112222mmHHLHH12212tan()mmmLHHHH210dXHXdx0dXdxcosmLx22122112mmHLHH1tanmmLH310dXHXdx0XsinmLx22122112mmHLHH1cotmmLH40dXdx20dXHXdxcosmx22222222mmHLHH2tanmmLH50dXdx0dXdxcosmx210:;0:0mLLsin0mL60dXdx0Xcosmx2Lcos0mL70X20dXHXdxsinmx22222222mmHLHH2cotmmLH80X0dXdxsinmx2Lcos0mL90X0Xsinmx2Lsin0mL对于这种特殊情况,00也是一个特殊值,对应于=1表2‐3边界条件为下列表格所示,微分方程为:222()()0dXxXxdx0x时的解(,)Xx及范数()N序号x=0处的边界条件(,)Xx1/()N110dXHXdx1cossinxHx22121H20dXdxcosx230Xsinx2