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 ...
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...
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...
Exact equations are first-order differential equations that appear in the form of $\boldsymbol{P(x, y) \phantom{x} +Q(x, y) \phantom{x} \phantom{x}dy = 0}$. We can solve exact equations by utilizing the partial derivatives of $\boldsymbol{P}$ and $\boldsymbol{Q}$....
In this paper I solved three first-order ordinary differential equations (ode) both analytically and numerically using 4 th order Runge-Kutta method (RK4). I selected differential equations which can also be solved analytically so as to compare the numerical solutions with the analytical solutions ...
E. Kulagin, “Exact First-Order Solutions of the Non-Linear Schrodinger Equation,” Theor. and Math. Phys. 72 (2), 809–818 (1987). MathSciNet ADS MATHAkhmediev, NN, Eleonskii, VM & Kulagin, NE 1987 Exact first-order solutions of the nonlinear Schro¨dinger equation. Theor. Math. ...
First-order differential equations can be expressed in the general form M(x,y)+N(x,y)y'=0. The equation is exact if M=dF/dx and N=dF/dy for some potential function F(x,y). Register to view this lesson Are you a student or a teacher?
order dispersive nonlinear Schrodinger equation sub-ODE Riccati equation exact solution PERIODIC-WAVE SOLUTIONS JACOBI ELLIPTIC FUNCTION SATSUMA COUPLED KDV KADOMTSEV-PETVIASHVILI EQUATION VARIANT BOUSSINESQ EQUATIONS NOVIKOV-VESELOV EQUATION EXTENDED TANH-FUNCTION BROER-KAUP EQUATIONS F-EXPANSION METHOD OPTICAL ...
Such as, the subequation method =-=[2,5,6,14]-=-, the exp-function method [16], the first integral method [11,15], the complex transform method [12] and so on. The common of these methods is based on the homogenous balance principle. In this study,...Zheng B, Wen C. Exact ...