序号.

$\varphi \left(\xi \right)$

条件

1

$-\frac{B+\sqrt{\Delta }}{2C}\tanh \left(\frac{\sqrt{\Delta }}{2}\xi \right)$

$\Delta >0$

2

$-\frac{B+\sqrt{\Delta }}{2C}\coth \left(\frac{\sqrt{\Delta }}{2}\xi \right)$

$\Delta >0$

3

$-\frac{B-\sqrt{-\Delta }}{2C}\tan \left(\frac{\sqrt{-\Delta }}{2}\xi \right)$

$\Delta <0$

4

$-\frac{B-\sqrt{-\Delta }}{2C}\cot \left(\frac{\sqrt{-\Delta }}{2}\xi \right)$

$\Delta <0$

5

$-\frac{1}{C\xi +H_1}$

$A=B=0,C\ne 0$