isolate terms - Maple Help

isolate

isolate a subexpression to left side of an equation

 Calling Sequence isolate(eqn, expr) isolate(eqn, expr, iter)

Parameters

 eqn - equation or algebraic expression expr - any algebraic expression iter - (optional) positive integer

Description

 • The procedure isolate attempts to isolate the second argument expr in the first argument eqn and solves eqn for expr.
 • If eqn is an equation (=) or inequation (<>) then isolate attempts to put expr on the left-hand side. If eqn is an inequality then isolate may put expr on the right- or left-hand side whichever isolates expr more completely.
 • If the first argument is not a relation, then the equation $\mathrm{eqn}=0$ is assumed.
 • The optional third argument iter controls the maximum number of transformation steps that isolate performs.  The default is 100000.
 • For direct solutions of equations, solve may be more efficient than isolate, which is intended, primarily, for use in an interactive Maple session.
 • Furthermore, whereas isolate returns an equation equivalent to its input, solve returns solutions to its input equations, and can handle systems of equations with multiple solutions.

Examples

 > $\mathrm{isolate}\left(4x\mathrm{sin}\left(x\right)=3,\mathrm{sin}\left(x\right)\right)$
 ${\mathrm{sin}}{}\left({x}\right){=}\frac{{3}}{{4}{}{x}}$ (1)
 > $\mathrm{isolate}\left(2x+1\le 6,x\right)$
 ${x}{\le }\frac{{5}}{{2}}$ (2)
 > $\mathrm{isolate}\left(-2x+1\le 0,x\right)$
 $\frac{{1}}{{2}}{\le }{x}$ (3)
 > $\mathrm{isolate}\left({x}^{2}-3x-5,{x}^{2}\right)$
 ${{x}}^{{2}}{=}{3}{}{x}{+}{5}$ (4)
 > $\mathrm{isolate}\left({x}^{2}-3x-5,x,0\right)$
 ${{x}}^{{2}}{-}{3}{}{x}{-}{5}{=}{0}$ (5)
 > $\mathrm{isolate}\left({x}^{2}-3x-5,x,1\right)$
 ${{x}}^{{2}}{-}{3}{}{x}{=}{5}$ (6)
 > $\mathrm{isolate}\left({x}^{2}-3x-5,x,2\right)$
 ${x}{=}\frac{{3}}{{2}}{-}\frac{\sqrt{{29}}}{{2}}$ (7)
 > $\mathrm{isolate}\left({x}^{2}-3x-5,x\right)$
 ${x}{=}\frac{{3}}{{2}}{-}\frac{\sqrt{{29}}}{{2}}$ (8)
 > $\mathrm{solve}\left({x}^{2}-3x-5,x\right)$
 $\frac{{3}}{{2}}{+}\frac{\sqrt{{29}}}{{2}}{,}\frac{{3}}{{2}}{-}\frac{\sqrt{{29}}}{{2}}$ (9)

Note that isolate does not perform integration or differentiation to isolate for expr.

 > $p\left(\frac{ⅆ}{ⅆx}h\left(x\right)\right)+w+∫h\left(x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}ⅆx=s\left(x\right)$
 ${p}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{h}{}\left({x}\right)\right){+}{w}{+}{\int }{h}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}{=}{s}{}\left({x}\right)$ (10)
 > $\mathrm{isolate}\left(,h\left(x\right)\right)$
 ${p}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{h}{}\left({x}\right)\right){+}{\int }{h}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}{=}{s}{}\left({x}\right){-}{w}$ (11)