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- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_420%3A_Differential_Equations_(Breitenbach)/02%3A_First_Order_Equations/2.02%3A_Exact_Equations\( \newcommand{\place}{\bigskip\hrule\bigskip\noindent} \newcommand{\threecol}[3]{\left[\boldsymbol{\begin{array}{r}#1\\#2\\#3\end{array}}\right]} \newcommand{\threecolj}[3]{\left[\begin{array}{r}#1\\[1\jot]#2\\[1...\( \newcommand{\place}{\bigskip\hrule\bigskip\noindent} \newcommand{\threecol}[3]{\left[\boldsymbol{\begin{array}{r}#1\\#2\\#3\end{array}}\right]} \newcommand{\threecolj}[3]{\left[\boldsymbol{\begin{array}{r}#1\\[1\jot]#2\\[1\jot]#3\end{array}}\right]} \newcommand{\lims}[2]{\,\bigg|_{#1}^{#2}} \newcommand{\twocol}[2]{\left[\boldsymbol{\begin{array}{l}#1\\#2\end{array}}\right]} \newcommand{\ctwocol}[2]{\left[\boldsymbol{\begin{array}{c}#1\\#2\end{array}}\right]} \newcommand{\cthreecol}[3]{\left[\boldsymbol{\begin{array}{c}#1\\#2\\#3\end{array}}\right]} \newco…
- https://math.libretexts.org/Bookshelves/Analysis/Supplemental_Modules_(Analysis)/Ordinary_Differential_Equations/2%3A_First_Order_Differential_Equations/2.7%3A_Exact_Differential_EquationsThat is if a differential equation can be written in a specific form, then we can seek the original function f(x,y) (called a potential function). A differential equation with a potential function is...That is if a differential equation can be written in a specific form, then we can seek the original function f(x,y) (called a potential function). A differential equation with a potential function is called exact. If you have had vector calculus, this is the same as finding the potential functions and using the fundamental theorem of line integrals.
- https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/4%3A_Integration_in_Vector_Fields/4.5%3A_Path_Independence%2C_Conservative_Fields%2C_and_Potential_FunctionsFor certain vector fields, the amount of work required to move a particle from one point to another is dependent only on its initial and final positions, not on the path it takes. Gravitational and el...For certain vector fields, the amount of work required to move a particle from one point to another is dependent only on its initial and final positions, not on the path it takes. Gravitational and electric fields are examples of such vector fields. This section will discuss the properties of these vector fields.
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_2562_Differential_Equations_with_Linear_Algebra/02%3A_First_Order_Equations/2.05%3A_Exact_EquationsThis section covers exact differential equations, which are given this name because the method for solving them uses the idea of an exact differential from calculus.
- https://math.libretexts.org/Courses/Mission_College/Math_4B%3A_Differential_Equations_(Reed)/02%3A_First_Order_Equations/2.05%3A_Exact_EquationsThis section covers exact differential equations, which are given this name because the method for solving them uses the idea of an exact differential from calculus.
- https://math.libretexts.org/Courses/Red_Rocks_Community_College/MAT_2561_Differential_Equations_with_Engineering_Applications/02%3A_First_Order_Equations/2.06%3A_Exact_EquationsThis section covers exact differential equations, which are given this name because the method for solving them uses the idea of an exact differential from calculus.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/02%3A_First_Order_Equations/2.05%3A_Exact_EquationsThis section covers exact differential equations, which are given this name because the method for solving them uses the idea of an exact differential from calculus.
- https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/04%3A_Line_and_Surface_Integrals/4.01%3A_Line_IntegralsIn this section, we will see how to define the integral of a function (either real-valued or vector-valued) of two variables over a general path (i.e. a curve) in R2 . This definition wi...In this section, we will see how to define the integral of a function (either real-valued or vector-valued) of two variables over a general path (i.e. a curve) in R2 . This definition will be motivated by the physical notion of work. We will begin with real-valued functions of two variables.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/02%3A_First_Order_Equations/2.06%3A_Exact_EquationsThis section covers exact differential equations, which are given this name because the method for solving them uses the idea of an exact differential from calculus.
- https://math.libretexts.org/Courses/Chabot_College/Math_4%3A_Differential_Equations_(Dinh)/02%3A_First_Order_Equations/2.06%3A_Exact_EquationsThis section covers exact differential equations, which are given this name because the method for solving them uses the idea of an exact differential from calculus.
- https://math.libretexts.org/Courses/Mission_College/Math_4B%3A_Differential_Equations_(Kravets)/02%3A_First_Order_Equations/2.05%3A_Exact_EquationsThis section covers exact differential equations, which are given this name because the method for solving them uses the idea of an exact differential from calculus.
