Wolfram equation solver

Built into the Wolfram Language is the world's largest collection of both numerical and symbolic equation solving capabilities — with many original algorithms, all automatically accessed through a small number of exceptionally powerful functions.

Wolfram Alpha is a great tool for finding polynomial roots and solving systems of equations. It also factors polynomials, plots polynomial solution sets and inequalities and more. Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to formulate queries.

Wolfram equation solver

Solve [ expr , vars ]. Solve [ expr , vars , dom ]. Common choices of dom are Reals , Integers , and Complexes. Solve simultaneous equations in and :. Plot the real parts of the solutions for y as a function of the parameter a :. Solution of this equation over the reals requires conditions on the parameters:. Use Normal to remove the conditions:. Solution of this equation over the positive integers requires introduction of a new parameter:. By default, Solve uses Root objects to represent solutions of general cubic equations with numeric coefficients:. Here Solve finds some solutions but is not able to prove there are no other solutions:. Equation with a purely imaginary period over a vertical stripe in the complex plane:. Systems exp-log in the first variable and polynomial in the other variables:. Systems elementary and bounded in the first variable and polynomial in the other variables:. Systems analytic and bounded in the first variable and polynomial in the other variables:. The answer depends on the parameter value :.

Method 1 By default, Solve uses inverse functions to solve non-polynomial complex equations:.

Wolfram Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints. Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask about solving systems of equations. Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator.

Solve [ expr , vars ]. Solve [ expr , vars , dom ]. Common choices of dom are Reals , Integers , and Complexes. Solve simultaneous equations in and :. Plot the real parts of the solutions for y as a function of the parameter a :.

Wolfram equation solver

Wolfram Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints. Enter your queries using plain English.

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The answer depends on the parameter value :. ParametricNDSolve — numerical solution to differential equations with parameters. Similar remarks hold for working with systems of inequalities: the linear case can be handled using methods covered in linear algebra courses, whereas higher-degree polynomial systems typically require more sophisticated computational tools. VerifySolutions 1 Solve verifies solutions obtained using non-equivalent transformations:. By default, Solve finds exact solutions of equations:. Solve gives generic solutions only. Details and Options. Use Reduce to get all solutions:. Solve verifies solutions obtained using non-equivalent transformations:. There are more advanced formulas for expressing roots of cubic and quartic polynomials, and also a number of numeric methods for approximating roots of arbitrary polynomials. This includes elimination, substitution, the quadratic formula, Cramer's rule and many more. More advanced methods are needed to find roots of simultaneous systems of nonlinear equations. Learn how.

Wolfram Alpha can apply the quadratic formula to solve equations coercible into the form. In doing so, Wolfram Alpha finds both the real and complex roots of these equations.

Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator. GeneratedParameters 1 Solve may introduce new parameters to represent the solution:. Systems elementary and bounded in the first variable and polynomial in the other variables:. Equation with a purely imaginary period over a vertical stripe in the complex plane:. Solve results do not depend on whether some of the input equations contain only parameters. One learns about the "factor theorem," typically in a second course on algebra, as a way to find all roots that are rational numbers. The Wolfram Language's symbolic architecture allows both equations and their solutions to be conveniently given in symbolic form, and immediately integrated into computations and visualizations. WorkingPrecision 1 By default, Solve finds exact solutions of equations:. Use FunctionAnalytic to test whether a function is analytic:. Systems with Mixed Variable Domains 2 Mixed real and complex variables:. Use RSolve to solve recurrence equations:. Here the removable singularity at is cancelled by Together , which is used to preprocess the equation:. ForAll [ x , cond , expr ]. Use Series to compute series expansions of Root objects:.