如果你也在 怎样代写微分方程differential equation这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。微分方程differential equation在数学中,是将一个或多个未知函数及其导数联系起来的方程。在应用中,函数通常代表物理量,导数代表其变化率,而微分方程则定义了两者之间的关系。这种关系很常见;因此,微分方程在许多学科,包括工程、物理学、经济学和生物学中发挥着突出作用。
微分方程differential equation研究主要包括研究其解(满足每个方程的函数集合),以及研究其解的性质。只有最简单的微分方程可以用明确的公式求解;然而,一个给定的微分方程的解的许多属性可以在不精确计算的情况下确定。
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数学代写|微分方程代写differential equation代考|Analytical solutions of simple differential equations
Function dsolve() is provided in MATLAB Symbolic Math Toolbox. It can be used in finding analytical solutions of ordinary differential equations. With such a tool, different complicated differential equations can be handled directly. If a certain differential equation is shown to have no analytical solutions, numerical methods should be used instead to solve it.
The syntaxes of dsolve() function are
sols $=$ dsolve $\left(f_{1}, f_{2}, \ldots, f_{m}\right), \%$ default independent variable $t$ $y=$ dsolve $\left(f_{1}, f_{2}, \ldots, f_{m}\right.$, varlist $)$, \%indicate the independent variable $[x, y, \ldots]=$ dsolve $\left(f_{1}, f_{2}, \ldots, f_{m}\right.$, varlist $)$, \%indicate return variables list
In the earlier versions of MATLAB, $f_{i}$ could be expressed by both symbolic expressions and strings, to describe the equations and known conditions. In the current and subsequent versions, less support is provided for string expressions. The focus is on symbolic expression description and solutions.
数学代写|微分方程代写differential equation代考|Analytical solutions of high-order linear differential equations with constant coefficients
The function dsolve () discussed earlier can be applied directly in solving high-order linear differential equations with constant coefficients, or any other form of complicated differential equations. The differential equations and given conditions should be expressed directly so that the function can be called to find the analytical solutions. In the earlier versions, strings could be used to describe the differential equations, while in a future version, the string description might not be supported.
To concisely describe the differential equation and given conditions, intermediate variables can be defined to record the derivatives of $y(t)$. The definition of the intermediate variables will be demonstrated through examples.
Example 2.20. Solve again the differential equation in Example $2.14$ with the unified solver and compare the results.
数学代写|微分方程代写DIFFERENTIAL EQUATION代考|Analytical solutions of linear time-varying differential equations
The direct solution method was demonstrated for linear differential equations with constant coefficients. If the coefficients are functions of the independent variable, and the variable is regarded as time, the differential equation is known as a timevarying one. Time-varying differential equations can also be explored with the solver dsolve (). Several examples are given next to demonstrate direct solutions of timevarying differential equations.
Example 2.25. Solve the following second-order time-varying differential equation:
$$
y^{\prime \prime}(x)+a y^{\prime}(x)+(b x+c) y(x)=0 .
$$
微分方程代写
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