fsolve
solve one or more equations using floatingpoint arithmetic
Calling Sequence
Parameters
Basic Information
Examples
Details
fsolve( equations, variables, complex )
equations

equation, set(equation), expression, set(expression), list(equation), procedure, list(procedure)
variables
(optional) name or set(name); unknowns for which to solve
complex
(optional) literal name; search for complex solutions
Description
The fsolve command numerically computes the zeroes of one or more equations, expressions or procedures.
Output
The solutions to a single equation are returned as an expression sequence.
The solutions to a set or list of equations are returned as sets of equation sequences.
For a single polynomial equation of one variable with real coefficients, by default the fsolve command computes all real (noncomplex) roots. It may not return all roots for exceptionally illconditioned polynomials.
For a single polynomial equation of one variable with some (nonreal) complex coefficients, the fsolve command computes all real and complex roots. It may not return all roots for exceptionally illconditioned polynomials.
For a general equation or system of equations, the fsolve command computes a single real root.
A Polynomial Equation in One Variable
For a univariate real polynomial equation, the fsolve command computes all real solutions.
$\mathrm{polynomial}\u22542{x}^{5}11{x}^{4}7{x}^{3}+12{x}^{2}4x=0\:$
$\mathrm{fsolve}\left(\mathrm{polynomial}\right)$
${\mathrm{1.334383488}}{,}{0.}{,}{5.929222024}$
Other Equations
For more complicated equations, the fsolve command computes one real solution.
$\mathrm{polynomials}\u2254\left\{3{x}^{4}{y}^{2}=17\,{x}^{3}y5x{y}^{2}2y=1\right\}\:$
$\mathrm{fsolve}\left(\mathrm{polynomials}\right)$
$\left\{{x}{=}{2.118203038}{\,}{y}{=}{0.5305528603}\right\}$
$\mathrm{fsolve}\left(\mathrm{tan}\left(\mathrm{sin}\left(x\right)\right)=1\right)$
${0.9033391108}$
$f\u2254\mathrm{sin}\left(x+y\right)\mathrm{exp}\left(x\right)y=0\:$
$g\u2254{x}^{2}y=2\:$
$\mathrm{fsolve}\left(\left\{f\,g\right\}\right)$
$\left\{{x}{=}{\mathrm{6.017327250}}{\,}{y}{=}{34.20822723}\right\}$
If an equation has no real solutions or you are interested in complex solutions then you can search for a complex solution using the complex option. For equations and expressions, the complex option must be preceded by the variables option.
$\mathrm{fsolve}\left(\mathrm{ln}\left(v\right)={v}^{2}\right)$
${\mathrm{fsolve}}{}\left({\mathrm{ln}}{}\left({v}\right){=}{{v}}^{{2}}{\,}{v}\right)$
$\mathrm{fsolve}\left(\mathrm{ln}\left(v\right)={v}^{2}\,v\,\mathrm{complex}\right)$
${0.6143632454}{}{0.6810654878}{}{\mathrm{I}}$
$\mathrm{fsolve}\left(\mathrm{ln}\left(v\right){v}^{2}\,v\,\mathrm{complex}\right)$
$\mathrm{fsolve}\left(t\mapsto \mathrm{ln}\left(t\right){t}^{2}\,\mathrm{complex}\right)$
For detailed information including:
Complete description of all parameters
Complete description of functionality
Specifying ranges or initial points
Shortcuts for specifying equations and unknowns
Specifying you want to find complex roots
Limiting the number of solutions returned for a polynomial equation of one variable
see the fsolve/details help page.
See Also
Digits
dsolve/numeric
Numeric Computation in Maple
pdsolve/numeric
RootFinding[Analytic]
RootFinding[Isolate]
solve
Download Help Document
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