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We say that a function is a solution to a differential equation if, when we plug it (and its various derivatives) into the equation, we find that the equation is satisfied.
A number is a solution when it fits within the range of answers that the function generates. For differential equations an equation is a solution when the equation is created satisfies the derivative's range.
In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
The general solution encompasses all solutions, and a particular solution is just one of those. It always occurs when you are solving differential equations. Its physical significance is that the particular solution solves the equation, but may not satisfy the initial conditions you are interested in.
An ordinary differential equation (ODE) is an equation that involves some ordinary derivatives (as opposed to partial derivatives) of a function. Often, our goal is to solve an ODE, i.e., determine what function or functions satisfy the equation. In general, solving an ODE is more complicated than simple integration.
Substitute y = UV, and. Factor the parts involving v. Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step) Solve using separation of variables to find u. Substitute u back into the equation we got at step 2. Solve that to find v.
Differential Equations Solutions: A solution of a differential equation is a relation between the variables (independent and dependent), which is free of derivatives of any order, and which satisfies the differential equation identically.
0:00 1:37 Suggested clip Differential Equations Determine if the Function is a Solution YouTubeStart of suggested client of suggested clip Differential Equations Determine if the Function is a Solution
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