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S = dsolve(eqn) solves the differential equation eqn, where eqn is a symbolic equation. Use diff and == to represent differential equations. For example, diff(y,x) == y represents the equation dy / dx = y .
- Examples
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- Matlab Dsolve
Differential equation or system of equations, specified as a...
- Examples
DSolve can solve ordinary differential equations (ODEs), partial differential equations (PDEs), differential algebraic equations (DAEs), delay differential equations (DDEs), integral equations, integro-differential equations, and hybrid differential equations.
DSolve [{eqn1,eqn2,…},{y1[x],y2[x],…},x] solve a system of differential equations for yi[x] Finding symbolic solutions to ordinary differential equations. DSolve returns results as lists of rules. This makes it possible to return multiple solutions to an equation.
- Introduction
- Setting Up The Problem
- Verification of The Solution
- Plotting The Solution
- Generated Parameters
- Holonomic Solutions
- Singular Solutions
- Assumptions
- Symbolic Parameters and Inexact Quantities
- Is The Problem Well-Posed?
The aim of these tutorials is to provide a self-contained working guide for solving different types of problems with DSolve. The first step in using DSolve is to set up the problem correctly. The next step is to use DSolve to get an expression for the solution. Once the solution has been found, it can be verified using symbolic or numerical techniq...
The first argument given to DSolveis the differential equation, the second argument is the unknown function, and the last argument identifies the independent variable. The output of DSolve is a list of solutions for the differential equation. The extra list is required since some equations have multiple solutions. Here, since the equation is of ord...
The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the solution is valid. Sometimes the result of the substitution is more complicated than True or False. Such examples can be verified by using Simplify to simplify the result of the...
A plot of the solution given by DSolvecan give useful information about the nature of the solution, for instance, whether it is oscillatory in nature. It can also serve as a means of solution verification if the shape of the graph is known from theory or from plotting the vector field associated with the differential equation. A few examples that u...
The general solution to a differential equation contains undetermined coefficients that are labeled C, C, and so on. To change the name of the undetermined parameter, use the GeneratedParametersoption. The parameter C should be thought of as a pure function that acts on a set of indices to generate different constants C[i]. Internally, the use of a...
The solutions of linear ODEs with polynomial or rational function coefficients can be expressed in terms of holonomic function DifferentialRoot. The option Method"Holonomic" forces DSolveto return a holonomic solution for a linear ODE.
By default, DSolvereturns a general solution depending on arbitrary parameters for a linear or nonlinear ODE. For some nonlinear ODEs, there can be also singular solutions. These singular solutions cannot be obtained by assigning specific values to the arbitrary constants in the general solution, but are useful in the study of dynamical systems and...
In some cases, ODEs have different solutions depending on specific types and ranges of parameters or variables. The Assumptions option in DSolveallows one to specify the types or ranges of parameters and variables to choose the necessary solution.
The differential equations that arise in practice are of two types. 1. Equations in which the only variables are the independent and dependent variables. Thus, all the variables that appear in the first argument to DSolveare also in the second or third arguments. 2. Equations in which there are other symbolic quantities, such as mass or the spring ...
DSolvereturns a general solution for a problem if no initial or boundary conditions are specified. However, if initial or boundary conditions are specified, the output from DSolvemust satisfy both the underlying differential equation as well as the given conditions. In such cases, it is useful to check whether DSolve has been asked a reasonable que...
For one equation and one output, dsolve returns the resulting solution with multiple solutions to a nonlinear equation in a symbolic vector. For several equations and an equal number of outputs, dsolve sorts the results alphabetically and assigns them to the outputs.
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The Mathematica function DSolve finds symbolic solutions to differential equations. (The Mathe-matica function NDSolve, on the other hand, is a general numerical differential equation solver.) DSolve can handle the following types of equations: † Ordinary Differential Equations (ODEs), in which there is a single independent variable t and
Solve a differential equation analytically by using the dsolve function, with or without initial conditions.
