for some function {eq}F(x,y) {/eq}. In this case, the equation can be re-expressed as follows: Solving Exact Differential Equations Exact Differential Equations Examples Lesson Summary Frequently Asked Questions What are some examples of exact differential equations?
(x, y) = x, the differential equation dy dx + y +2 x x = 0 has solutions y(x) given by xy(x) + x 2 = ˆ c. Renaming ˆ c as −c and solving for y(x) we have y(x) = y(x, c) = c − x 2 x . To verify that this is the general solution we observe...
Exact differential equation is a type of differential equation there exists a function of two variables with continuous partial derivatives with integrating factor.
Differential Equation General Solution Same as the above multiplied by the integrating factor . Integrating Factors In solving "exactable" ordinary differential equations, the following table of common exact differential forms may help. Exact Differential Form Integrating Factor - - The above table also...
The best way to master solving exact equations is by working on different types of differential equations. Why don’t we begin by finding the solution for the differential equation, 4xydx+(2x2+8y2)dy=0? When given a differential equation, we first confirm the exactness of the differential ...
In the last decades Exp-function method has been used for solving fractional differential equations. In this paper, we obtain exact solutions of fractional generalized reaction Duffing model and nonlinear fractional diffusionu2013reaction equation. The fractional derivatives are described in the modified ...
Comment on: "A novel approach for solving the Fisher equation using Exp-function method" [Phys. Lett. A 372 (2008) 3836] The efficiency of application of Exp-function method to search for exact solutions of nonlinear differential equations is questioned by us... NA Kudryashov - 《Physics...
An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey systemexp(-Φ(ξ))-expansion methodThe diffusive predator–prey systemThe nonlinearBogoyavlenskii equationExact solutions...
curves represent the paths along which the solution of the PDE remains constant. The method of characteristics is a powerful technique for solving first-order partial differential equations (PDEs), including linear first-order PDEs such as the transport equation or the linear advection equation. ...
The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations. An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansatz and Backlund transf... Jianping,Zhao - 《Mathematical Problems in Engineering》 被...