\setcounter{figure}{0} \setcounter{equation}{0} \voffset=-0.2in \numberwithin{equation}{section}

以下是设置公式计数器和页边距的示例代码：

% 设置公式计数器
\setcounter{equation}{0}
\numberwithin{equation}{section}

% 设置页边距
\voffset=-0.2in

其中，`\setcounter{equation}{0}`将公式计数器重置为0，`\numberwithin{equation}{section}`将公式计数器设置为按照章节编号计数。`\voffset=-0.2in`将页面顶部的边距向上移动0.2英寸。

相关问题

Solve the equation x"+9x=-35(t-三). x(0)=1, x'(0）=0

We can start by finding the characteristic equation, which is:

r^2 + 9 = 0

Solving for r, we get:

r = ±√(-9) = ±3i

Therefore, the general solution to the homogeneous equation x" + 9x = 0 is:

x(t) = c1cos(3t) + c2sin(3t)

To find a particular solution to the non-homogeneous equation x" + 9x = -35(t-三), we can use the method of undetermined coefficients. Since the right-hand side is a linear function of t, we can guess a particular solution of the form:

x(t) = At + B

Taking the derivatives, we get:

x'(t) = A
x"(t) = 0

Substituting into the original equation, we get:

0 + 9(At+B) = -35(t-三)

Simplifying and equating coefficients, we get:

9A = -35
9B = -35三

Solving for A and B, we get:

A = -35/9
B = (-35三)/9

Therefore, the general solution to the non-homogeneous equation is:

x(t) = c1cos(3t) + c2sin(3t) - (35/9)t + (-35三/9)

Using the initial conditions x(0) = 1 and x'(0) = 0, we can solve for the constants c1 and c2:

x(0) = 1 = c1cos(0) + c2sin(0) - (35/9)(0) + (-35三/9)
1 = c1

x'(0) = 0 = -3c1sin(0) + 3c2cos(0) - 35/9
0 = 3c2 - 35/9

Solving for c1 and c2, we get:

c1 = 1
c2 = 35/27

Therefore, the solution to the initial value problem is:

x(t) = cos(3t) + (35/27)sin(3t) - (35/9)t - (35三/9)

\left\{ \begin{array}{rl} \begin{equation} G_1=-m_1g\\ T_1=k_1l=G_2=-m_2g\\ F_b=\rho(\frac{1}{3}$\pi$r^2)g \end{equation} \end{array} \right. \] 帮我修改一下这段代码

这段代码中存在一些错误的使用方式，我会为你进行修改：

\[
\left\{
\begin{array}{rl}
G_1=-m_1g\\
T_1=k_1l=G_2=-m_2g\\
F_b=\rho \left(\frac{1}{3}\pi r^2\right)g
\end{array}
\right.
\]

修改后的代码中，我将 `\begin{equation}...\end{equation}` 替换为简单的数学模式 `\[...\]`，并修正了其中的一些错误。请注意，`\left\{` 和 `\right.` 是用来显示大括号的配对命令。

现在，这段代码应该可以正确显示出等式组了。