![]() ![]() A unique feature of NDSolve is that given PDEs and the solution domain in symbolic form, NDSolve automatically chooses numerical methods that appear best suited to the problem structure. The following table introduces the types of equations that can be solved by DSolve. The Wolfram Language function NDSolve has extensive capability for solving partial differential equations (PDEs). ![]() Of these four areas, the study of exact solutions has the longest history, dating back to the period just after the discovery of calculus by Sir Isaac Newton and Gottfried Wilhelm von Leibniz. Existence and uniqueness theorems, which guarantee that there are solutions with certain desirable properties provided a set of conditions is fulfilled by the differential equation. Get the free 'General Differential Equation Solver' widget for your website, blog, Wordpress, Blogger, or iGoogle.Qualitative theory, which is concerned with the global properties of solutions and is particularly important in the modern approach to dynamical systems. Wolfram Alpha used to solve a differential equation based on initial conditions.Numerical solutions, which are available for a wider class of problems, but are typically only valid over a limited range of the independent variables.Exact solutions, which are closed-form or implicit analytical expressions that satisfy the given problem.where is a function of, is the first derivative with respect to, and is the th derivative with respect to. An ODE of order is an equation of the form. ![]() There are four major areas in the study of ordinary differential equations that are of interest in pure and applied science. An ordinary differential equation (frequently called an 'ODE,' 'diff eq,' or 'diffy Q') is an equality involving a function and its derivatives. ![]()
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