Providing analytical and numerical solutions to differential equations continues to be an important component of our research and development, this family of problems is of particular interest to us and will be the focus of future updates to the Wolfram Language and Mathematica functionality. I am in general very much like to explore more in MMA. But for my research purpose at the moment, I will have to stick with Maple, because it is the only Computer Algebraic package that gives me what I need.
The PDEs actually form from a null space of particular matrices. So in practice, I demand much more than this "simple" and small example. Wolfram Language Revolutionary knowledge-based programming language. Wolfram Science Technology-enabling science of the computational universe. Wolfram Notebooks The preeminent environment for any technical workflows. Wolfram Engine Software engine implementing the Wolfram Language. Wolfram Data Framework Semantic framework for real-world data.
Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. Wolfram Knowledgebase Curated computable knowledge powering Wolfram Alpha. Answer Unmark. Mark as an Answer. DSolve does not solve this.
Casper YC, Kent. Posted 6 years ago. Follow this post. Hi all, I am switching from Maple slowly to Mathematica.
This is just a "small" example I took. In my work sheet, I have attached the problematic PDE. I am not sure whether it's the double subscripts that I have used, so I tried to change to a set of simpler variables.
Mark as an Answer Reply Flag.
Udo Krause, NOrganization. Many thanks! Frankly spoken, I do not see it. The net knows, that one has to tinker a bit in the case of a partial differential equations system under Mma, compare e. However, it is only a "small" system i used to adress the problem here.
I have many and much larger PDE systems, which were formed from my research problems. So I dont think my focus is on the PDE here. If I have the time, I will stick with Maple for this matter. Because Maple works.
I tried the example on stackexchange. In my case, it does not work.Wolfram Language Revolutionary knowledge-based programming language. Wolfram Science Technology-enabling science of the computational universe. Wolfram Notebooks The preeminent environment for any technical workflows. Wolfram Engine Software engine implementing the Wolfram Language. Wolfram Data Framework Semantic framework for real-world data.
The Mathematica function NDSolve, on the other hand, is a general numerical differential equation solver. DSolve can handle ordinary differential equations, partial differential equations, and differential-algebraic equations. Drawn from the in-product documentation of Mathematica, the title Tutorial Collection gives users targeted instruction on the functions, capabilities, and unified architecture of the Mathematica system.
The Collection discontinued printing as of Januarybut the Mathematica 7 edition of each title remains available for download as a PDF. Wolfram Technology. Wolfram Mathematica Tutorial Collection:.The Wolfram Language function DSolve finds symbolic solutions to differential equations. The Wolfram Language function NDSolveon the other hand, is a general numerical differential equation solver.
DSolve can handle the following types of equations:. 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.
For a system of equations, possibly multiple solution sets are grouped together. You can use the rules to substitute the solutions into other calculations. A general solution contains arbitrary parameters C [ i ] that can be varied to produce particular solutions for the equation. When an adequate number of initial conditions is specified, DSolve returns particular solutions to the given equations. Finding symbolic solutions to ordinary differential equations as pure functions.
When the second argument to DSolve is specified as y instead of y [ x ]the solution is returned as a pure function. This form is useful for verifying the solution of the ODE and for using the solution in further work. More details are given in "Setting Up the Problem". Finding symbolic solutions to partial differential equations. While general solutions to ordinary differential equations involve arbitrary constantsgeneral solutions to partial differential equations involve arbitrary functions.
DSolve labels these arbitrary functions as C [ i ]. DSolve can also solve differential-algebraic equations. The syntax is the same as for a system of ordinary differential equations.
The design of DSolve is modular: the algorithms for different classes of problems work independently of one another. Once a problem has been classified as described in "Classification of Differential Equations"the available methods for that class are tried in a specific sequence until a solution is obtained.
The code has a hierarchical structure whereby the solution of complex problems is reduced to the solution of relatively simpler problems, for which a greater variety of methods is available. For example, higher-order ODEs are typically solved by reducing their order to 1 or 2.Secondly I'm trying to solve the heat equation with spherical coordinates but I have some issues in plotting the solution.
Here's my problem: I'm solving the heat equation with a spherical laplacian and I'm considering that the temperature only depends on the radius r.
Wolfram Language Revolutionary knowledge-based programming language. Wolfram Science Technology-enabling science of the computational universe. Wolfram Notebooks The preeminent environment for any technical workflows. Wolfram Engine Software engine implementing the Wolfram Language. Wolfram Data Framework Semantic framework for real-world data.
Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more.
Wolfram Knowledgebase Curated computable knowledge powering Wolfram Alpha. Answer Unmark. Mark as an Answer. DSolve: how to plot the heat equation solution? Olivier Lemarchand. Posted 5 years ago. Follow this post. Hi everyone First of all, sorry for my poor english, that's not my native language. Mark as an Answer Reply Flag.22 Curso Mathematica. Ecuaciones diferenciales
Sean Clarke, Wolfram Research. Dsolve returns a rule. Thank you very much for these explanations :. Reply to this discussion in reply to. Community posts can be styled and formatted using the Markdown syntax. Tag limit exceeded. Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles. Publish anyway Cancel.
Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It only takes a minute to sign up.
Do you have any ideas why Mathematica won't compute? Also, how should I modify my code to get some response? As commented by Mariusz Iwaniukthe initial conditions in the question are inconsistent. So, to understand the desired solution, first solve the equations numerically. The green curve represents zand the brown curve represents both x and ywhich are identical.
Moreover, x and y are identical whenever their initial conditions are identical. This fact allows the equations to be solved symbolically. The first two ODEs can be simplified by means of this first integral. The ODE system to be solved has been reduced from sixth to fourth order. Nonetheless, DSolve returns unevaluated from. Next, boundary conditions are imposed. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.
DSolve doesn't work Ask Question. Asked 3 years, 3 months ago. Active 4 days ago. Viewed 2k times. Thank you!For three decades, Mathematica has defined the state of the art in technical computing—and provided the principal computation environment for millions of innovators, educators, students, and others around the world. Widely admired for both its technical prowess and elegant ease of use, Mathematica provides a single integrated, continually expanding system that covers the breadth and depth of technical computing—and seamlessly available in the cloud through any web browser, as well as natively on all modern desktop systems.
With energetic development and consistent vision for three decades, Mathematica stands alone in a huge range of dimensions, unique in its support for today's technical computing environments and workflows.
Mathematica has nearly 5, built-in functions covering all areas of technical computing—all carefully integrated so they work perfectly together, and all included in the fully integrated Mathematica system.
Building on three decades of development, Mathematica excels across all areas of technical computing—including neural networks, machine learning, image processing, geometry, data science, visualizations, and much more. Mathematica builds in unprecedentedly powerful algorithms across all areas—many of them created at Wolfram using unique development methodologies and the unique capabilities of the Wolfram Language.
Superfunctions, meta-algorithms Mathematica provides a progressively higher-level environment in which as much as possible is automated—so you can work as efficiently as possible. Mathematica is built to provide industrial-strength capabilities—with robust, efficient algorithms across all areas, capable of handling large-scale problems, with parallelism, GPU computing, and more.
Mathematica draws on its algorithmic power—as well as the careful design of the Wolfram Language—to create a system that's uniquely easy to use, with predictive suggestions, natural language input, and more. Mathematica uses the Wolfram Notebook Interface, which allows you to organize everything you do in rich documents that include text, runnable code, dynamic graphics, user interfaces, and more.
With its intuitive English-like function names and coherent design, the Wolfram Language is uniquely easy to read, write, and learn. With sophisticated computational aesthetics and award-winning design, Mathematica presents your results beautifully—instantly creating top-of-the-line interactive visualizations and publication-quality documents.
Mathematica has access to the vast Wolfram Knowledgebasewhich includes up-to-the-minute real-world data across thousands of domains. The unique knowledge-based symbolic language that grew out of Mathematica, and now powers the Mathematica system. The world's largest integrated web of algorithms, providing broad and deep built-in capabilities for Mathematica. The uniquely flexible document-based interface that lets you mix executable code, richly formatted text, dynamic graphics, and interactive interfaces in Mathematica.
The core software system that implements the Wolfram Language—and Mathematica—across a wide range of local and cloud computational environments. The uniquely broad, continuously updated knowledgebase that powers Wolfram Alpha and supplies computable real-world data for use in Wolfram products. When Mathematica first appeared init revolutionized technical computing—and every year since then it's kept going, introducing new functions, new algorithms and new ideas.
Math was Mathematica's first great application area—and building on that success, Mathematica has systematically expanded into a vast range of areas, covering all forms of technical computing and beyond. Mathematica has followed a remarkable trajectory of accelerating innovation for three decades—made possible at every stage by systematically building on its increasingly large capabilities so far.
Versions of Mathematica aren't just incremental software updates; each successive one is a serious achievement that extends the paradigm of computation in new directions and introduces important new ideas. If you're one of the lucky people who used Mathematica 1, the code you wrote over three decades ago will still work—and you'll recognize the core ideas of Mathematica 1 in the vast system that is Mathematica today.
Mathematica has always stayed true to its core principles and careful design disciplines, letting it continually move forward and integrate new functionality and methodologies without ever having to backtrack. Wolfram Language Revolutionary knowledge-based programming language. Wolfram Science Technology-enabling science of the computational universe.
Wolfram Notebooks The preeminent environment for any technical workflows.Calling Sequence. These include the following. Using the assistant, you can compute numeric and exact solutions and plot the solutions. Solving an ODE. Define a simple ODE.
Solve the ODE, ode. Define initial conditions. Laplace Transform Method. Compute the solution using the Laplace transform method. Computing a Series Solution. Find a series solution for the same problem. Solving an ODE System. Define a system of ODEs. If the unknowns are not specified, all differentiated indeterminate functions in the system are treated as the unknowns of the problem.
Solve the system of ODEs subject to the initial conditions ics. See Also. ODE Analyzer Assistant. Download Help Document.
Online Help. Was this information helpful? Yes Somewhat No I would like to report a problem with this page. Tell us what we can do better:. Thanks for your Comment Thank you for submitting feedback on this help document. Your feedback will be used to improve Maple's help in the future. Examples Details. What kind of issue would you like to report?
Suggest new examples or content. Please add your Comment Optional. E-mail Address Optional. What is? This question helps us to combat spam.