$${\mathit{y}}^{\prime }=2\mathit{t}。$$

$$y_1^{\prime \prime }-\; -\; -\; -\; -\; -\mu (1-\; -\; -\; -\; -\; -y_1^2)y_1^{\prime }+y_1=0,$$

$$\begin{array}{cl}{y}_1^{\prime }& =y_2\\ y_2^{\prime }& =\mu (1-\; -\; -\; -\; -\; -y_1^2)y_2-\; -\; -\; -\; -\; -y_1。\end{array}$$

函数dydt = vdp1 (t, y)% VDP1评估μ= 1的范德堡尔常微分方程%%参见ODE113 ODE23,数值。% Jacek Kierzenka和劳伦斯·f·Shampine% 1984 - 2014版权MathWorks公司。dydt = [y (2);(1 y (1) ^ 2) * y (2) - y (1)];

$$y^{\prime \prime }=\frac{\mathrm{一个}}{B}ty。$$

$$\begin{array}{cl}{y}_1^{\prime }& =y_2\\ y_2^{\prime }& =\frac{\mathrm{一个}}{B}t{y}_1。\end{array}$$

函数dydt = odefcn (t y, B) dydt = 0 (2, 1);dydt (1) = y (2);dydt (2) = (A / B) * t。* y (1);结束

$$\begin{array}{l}{{\mathit{x}}^{\prime }}^{\prime }=-\; -\; -\; -\; -\; -\mathit{x}/{\mathit{r}}^3\\ {{\mathit{y}}^{\prime }}^{\prime }=-\; -\; -\; -\; -\; -\mathit{y}/{\mathit{r}}^3,\end{array}$$

$$\mathit{r}=\sqrt{{\mathit{x}}^2+{\mathit{y}}^2}。$$

$$\begin{array}{l}{\mathit{y}}_1=\mathit{x}\\ {\mathit{y}}_2={\mathit{x}}^{\prime }\\ {\mathit{y}}_3=\mathit{y}\\ {\mathit{y}}_4={\mathit{y}}^{\prime }。\end{array}$$

$$\begin{array}{l}{{\mathit{y}}_1}^{\prime }={\mathit{y}}_2\\ {{\mathit{y}}_2}^{\prime }=-\; -\; -\; -\; -\; -{\mathit{y}}_1/{\mathit{r}}^3\\ {{\mathit{y}}_3}^{\prime }={\mathit{y}}_4\\ {{\mathit{y}}_4}^{\prime }=-\; -\; -\; -\; -\; -{\mathit{y}}_3/{\mathit{r}}^3。\end{array}$$

函数dy = twobodyode (t, y)%双体与一个质量比另一个更大的问题。r =√(1) ^ 2 + y (3) ^ 2);dy = [y (2);- y (1) / r ^ 3;y (4);- y (3) / r ^ 3);结束