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Questions in category: MatLab (MatLab).

1

解微分方程组

Posted by haifeng on 2018-05-07 10:40:15 last update 2018-05-07 10:43:11 | Answers (0) | 收藏

解微分方程组

\[
\left\{
\begin{aligned}
y'_1&=y_2 y_3,\\
y'_2&=-y_1 y_3,\\
y'_3&=-0.51y_1 y_2,\\
y_1(0)&=0,\quad y_2(0)=1,\quad y_3(0)=1.
\end{aligned}
\right.
\]
 

2

求解微分方程 $x''(t)-1000(1-x^2)x'(t)+x=0$.

Posted by haifeng on 2018-05-04 08:29:06 last update 2018-05-07 10:25:31 | Answers (1) | 收藏

求解微分方程

\[
\begin{cases}
\dfrac{d^2 x}{dt^2}-1000(1-x^2)\dfrac{dx}{dt}+x(t)=0,\\
x(0)=0,\quad x'(0)=1.
\end{cases}
\]
 

 


[Hint]

将高阶微分方程转换为与之等价的一阶微分方程组.

 

 

References:

《数学建模与数学实验》(第四版)P.131

 

hello

3

求下列微分方程组的通解

Posted by haifeng on 2018-05-02 11:01:04 last update 2018-05-02 11:01:44 | Answers (1) | 收藏

求下列微分方程组的通解.

\[
\begin{cases}
\dfrac{dx}{dt}=2x-3y+3z,\\
\dfrac{dy}{dt}=4x-5y+3z,\\
\dfrac{dz}{dt}=4x-4y+2z.\\
\end{cases}
\]

 


References:

《数学建模与数学实验》(第四版)P.130

4

求下列微分方程 $y''+4y'+29y=0$ 的解.

Posted by haifeng on 2018-05-02 09:53:15 last update 2018-05-02 10:35:37 | Answers (2) | 收藏

求下列微分方程的解.

\[
\begin{cases}
\displaystyle\frac{d^2 y}{dx^2}+4\frac{dy}{dx}+29y=0,\\
y(0)=0,\quad y'(0)=15.
\end{cases}
\]

 


References:

《数学建模与数学实验》(第四版)P.130

5

求 $\dfrac{du}{dt}=1+u^2$ 的通解.

Posted by haifeng on 2018-05-01 18:52:58 last update 2018-05-02 09:53:28 | Answers (2) | 收藏

求 $\dfrac{du}{dt}=1+u^2$ 的通解.

 

[hint]

使用分离变量法求解.

 


进一步阅读

问题1959

Bernoulli 方程(伯努利方程)

 

References:

《数学建模与数学实验》(第四版)P.130

6

MatLab 入门

Posted by haifeng on 2011-06-28 09:58:42 last update 2011-06-28 11:17:09 | Answers (0) | 收藏


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