Consider a first-order ODE in the slightly different form p(x,y)dx+q(x,y)dy=0. (1) Such an equation is said to be exact if (partialp)/(partialy)=(partialq)/(partialx). (2) This statement is equivalent to the requirement that a conservative field
First Order Differential Equations. Exact Equations, Separation of Variables, Homogeneous and Linear EquationsAlthough it implements only a relatively small number of commands related to this topic, MATLAB's treatment of differential equations is nevertheless very efficient. We shall see how we can use...
first order differential equation exact differential equation examples some of the examples of the exact differential equations are as follows : ( 2xy – 3x 2 ) dx + ( x 2 –2y ) dy = 0 ( xy 2 + x ) dx + yx 2 dy = 0 cos y dx + ( y 2 –x sin y ) dy = 0 ( 6x 2 ...
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 shows that the integrating factors for a given exact differential form are not unique.Membershi...
A first‐order differential equation is one containing a first—but no higher—derivative of the unknown function. For virtually every such equation encountered in practice, the general solution will contain one arbitrary constant, that is, one parameter, so a first‐order IVP will contain one ini...
Exact equations are first-order differential equations that appear in the form of P(x,y)+Q(x,y)dy=0. We can solve exact equations by utilizing the partial derivatives of P and Q. Since this deals with differential equations, familiarity with the topic is a must. In this article, we’...
Part 1 First order differential equations: simplest equations with arbitrary functions integrable in a closed form Riccati equations - g(y)y'x=f2(x)y2+f1(x)y+f0(x) Abel equations of the second kind equations containing polynomial functions of y nonlinear equations of the form f(x,y)y'2...
Akhmediev, N.N., Eleonskii, V.M., Kulagin, N.E.: Exact first-order solutions of the nonlinear Schrodinger equation. Theor. Math. Phys. 72, 809-818 (1987)Akhmediev, N., Eleonskii, V. M. & Kulagin, N. E. (1987), `Exact first-order solutions of the nonlinear Schrdinger equation'...
We consider the first class of nonlinear second-order partial differential equations compilable in the following general form: utt+a(x,t)uxt+b(t)ut=α(x,t)+G(u)(ut+a(x,t)ux)e−∫b(t)dt, (1) whereudenotes a function of(x,t)∈R2. ...
It is easy to know that the travelling wave transformation u(ξ) = 2w(ξ), ξ = k(x − λt), b=αkλ reduces the famous sine-Gordon equation uxt = α sin u, which appears in many branches of nonlinear science [1], to the first-order ordinary differential equationdw(ξ)dξ=μ...