LinearForm - Maple Help
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Student[ODEs]

 LinearForm
 convert a first order ODE into linear form, if possible

 Calling Sequence LinearForm(ODE, y(x))

Parameters

 ODE - an ordinary differential equation y - name; the dependent variable x - name; the independent variable

Description

 • LinearForm(ODE, y(x)) outputs an equivalent linear ODE, if that is possible. If not, an error is produced.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{ODEs}}\right):$
 > $\mathrm{ode1}≔\frac{{t}^{2}\left(z\left(t\right)+1\right)}{z\left(t\right)}+\left(t-1\right)\left(\frac{ⅆ}{ⅆt}z\left(t\right)\right)={t}^{2}\left(z\left(t\right)+\frac{1}{z\left(t\right)}\right)$
 ${\mathrm{ode1}}{≔}\frac{{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}{1}\right)}{{z}{}\left({t}\right)}{+}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}\frac{{1}}{{z}{}\left({t}\right)}\right)$ (1)
 > $\mathrm{LinearForm}\left(\mathrm{ode1},z\left(t\right)\right)$
 $\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right){=}\frac{{{t}}^{{2}}{}{z}{}\left({t}\right)}{{t}{-}{1}}{-}\frac{{{t}}^{{2}}}{{t}{-}{1}}$ (2)
 > $\mathrm{ode2}≔{t}^{2}\left(z\left(t\right)+1\right)+{z\left(t\right)}^{2}\left(t-1\right)\left(\frac{ⅆ}{ⅆt}z\left(t\right)\right)=0$
 ${\mathrm{ode2}}{≔}{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}{1}\right){+}{{z}{}\left({t}\right)}^{{2}}{}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}{0}$ (3)
 > $\mathrm{LinearForm}\left(\mathrm{ode2},z\left(t\right)\right)$

Compatibility

 • The Student[ODEs][LinearForm] command was introduced in Maple 2021.
 • For more information on Maple 2021 changes, see Updates in Maple 2021.