solve - Maple Help

MTM

 solve
 solve equations

 Calling Sequence solve(eqn1,eqn2,...,eqnN); solve(eqn1,eqn2,...,eqnN, var1, var2,..., varN);

Parameters

 eqni - equations or algebraic expressions vari - variables

Description

 • solve(eqn1,...,eqnN) returns solutions to the system of equations with respect to variables found by findsym.
 • solve(eqn1,eqn2,...,eqnN, var1, var2,..., varN) returns solutions with respect to given variables.
 • If no closed-form solution is found and the number of equations is equal to number of variables, numeric solve is attempted.
 • Three different types of output are possible.  For one equation and one output, the resulting solution is returned with multiplicities for a polynomial equation in a vector.  For several variables and an equal number of outputs, the results are sorted and assigned to the outputs.  For several equations and a single output, a MTM[struct] containing the solutions is returned.

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $t≔2+{\left(3+4\mathrm{log}\left(x\right)\right)}^{2}-5\mathrm{log}\left(x\right):$
 > $\mathrm{solve}\left(t\right)$
 $\left[\begin{array}{c}{{ⅇ}}^{{-}\frac{{19}}{{32}}{+}\frac{{7}{}{I}{}\sqrt{{7}}}{{32}}}\\ {{ⅇ}}^{{-}\frac{{19}}{{32}}{-}\frac{{7}{}{I}{}\sqrt{{7}}}{{32}}}\end{array}\right]$ (1)
 > $\mathrm{solve}\left(p\mathrm{sin}\left(x\right)=r\right)$
 ${\mathrm{arcsin}}{}\left(\frac{{r}}{{p}}\right)$ (2)
 > $x,y≔\mathrm{solve}\left({x}^{2}+xy+y=3,{x}^{2}-4x+3=0\right)$
 ${x}{,}{y}{≔}\left[\begin{array}{c}{1}\\ {3}\end{array}\right]{,}\left[\begin{array}{c}{1}\\ {-}\frac{{3}}{{2}}\end{array}\right]$ (3)
 > $S≔\mathrm{solve}\left({u}^{2}{v}^{2}-2u-1=0,{u}^{2}-{v}^{2}-1=0\right):$
 > $S:-u$
 $\left[\begin{array}{c}{-}\frac{{1}}{{2}}{+}\frac{{I}{}\sqrt{{3}}}{{2}}\\ {-}\frac{{1}}{{2}}{+}\frac{{I}{}\sqrt{{3}}}{{2}}\\ {-}\frac{{1}}{{2}}{-}\frac{{I}{}\sqrt{{3}}}{{2}}\\ {-}\frac{{1}}{{2}}{-}\frac{{I}{}\sqrt{{3}}}{{2}}\\ \frac{\sqrt{{5}}}{{2}}{+}\frac{{1}}{{2}}\\ \frac{\sqrt{{5}}}{{2}}{+}\frac{{1}}{{2}}\\ {-}\frac{\sqrt{{5}}}{{2}}{+}\frac{{1}}{{2}}\\ {-}\frac{\sqrt{{5}}}{{2}}{+}\frac{{1}}{{2}}\end{array}\right]$ (4)
 > $S:-v$
 $\left[\begin{array}{c}\frac{\sqrt{{-}{6}{-}{2}{}{I}{}\sqrt{{3}}}}{{2}}\\ {-}\frac{\sqrt{{-}{6}{-}{2}{}{I}{}\sqrt{{3}}}}{{2}}\\ \frac{\sqrt{{-}{6}{+}{2}{}{I}{}\sqrt{{3}}}}{{2}}\\ {-}\frac{\sqrt{{-}{6}{+}{2}{}{I}{}\sqrt{{3}}}}{{2}}\\ \frac{\sqrt{{2}{+}{2}{}\sqrt{{5}}}}{{2}}\\ {-}\frac{\sqrt{{2}{+}{2}{}\sqrt{{5}}}}{{2}}\\ \frac{\sqrt{{2}{-}{2}{}\sqrt{{5}}}}{{2}}\\ {-}\frac{\sqrt{{2}{-}{2}{}\sqrt{{5}}}}{{2}}\end{array}\right]$ (5)
 > $S≔\mathrm{solve}\left(a{u}^{2}+{v}^{2},u-v=1,a,u\right):$
 > $S:-a$
 ${-}\frac{{{v}}^{{2}}}{{{v}}^{{2}}{+}{2}{}{v}{+}{1}}$ (6)
 > $S:-u$
 ${v}{+}{1}$ (7)
 > $a,u,v≔\mathrm{solve}\left(a{u}^{2}+{v}^{2},u-v=1,{a}^{2}-5a+6\right)$
 ${a}{,}{u}{,}{v}{≔}\left[\begin{array}{c}{2}\\ {2}\\ {3}\\ {3}\end{array}\right]{,}\left[\begin{array}{c}\frac{{1}}{{3}}{+}\frac{{I}{}\sqrt{{2}}}{{3}}\\ \frac{{1}}{{3}}{-}\frac{{I}{}\sqrt{{2}}}{{3}}\\ \frac{{1}}{{4}}{+}\frac{{I}{}\sqrt{{3}}}{{4}}\\ \frac{{1}}{{4}}{-}\frac{{I}{}\sqrt{{3}}}{{4}}\end{array}\right]{,}\left[\begin{array}{c}{-}\frac{{2}}{{3}}{+}\frac{{I}{}\sqrt{{2}}}{{3}}\\ {-}\frac{{2}}{{3}}{-}\frac{{I}{}\sqrt{{2}}}{{3}}\\ {-}\frac{{3}}{{4}}{+}\frac{{I}{}\sqrt{{3}}}{{4}}\\ {-}\frac{{3}}{{4}}{-}\frac{{I}{}\sqrt{{3}}}{{4}}\end{array}\right]$ (8)