Overview - Maple Help

Overview of the Student[ODEs][Solve] Command and Subpackage

 Calling Sequence Student[ODEs][Solve][command](arguments) command(arguments) Solve(ODE, y(x))

Parameters

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

Description

 • The Solve(ODE, y(x)) command finds the solution of an ordinary differential equation.
 • Student[ODEs][Solve] is also a subpackage containing a number of commands for solving ordinary differential equations and systems of ODEs.
 • Each command in the Student[ODEs][Solve] subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence.
 The long form, Student[ODEs][Solve]:-command or Student:-ODEs:-Solve:-command, is always available. The short form can be used after loading the package.
 • The Maple Command Completion facility is helpful for entering the names of Student package commands.

Computation

 The subpackage Student[ODEs][Solve] consists of commands for solving ODEs and systems according to various methods:

Getting Help with a Command in the Package

 To display the help page for a particular Student[ODEs][Solve] command, see Getting Help with a Command in a Package.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{ODEs}\right]\right):$
 > $\mathrm{ode1}≔{t}^{2}\left(z\left(t\right)+1\right)+{z\left(t\right)}^{2}\left(t-1\right)\mathrm{diff}\left(z\left(t\right),t\right)=0$
 ${\mathrm{ode1}}{≔}{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}{1}\right){+}{{z}{}\left({t}\right)}^{{2}}{}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}{0}$ (1)
 > $\mathrm{Solve}\left(\mathrm{ode1},z\left(t\right)\right)$
 $\frac{{{z}{}\left({t}\right)}^{{2}}}{{2}}{-}{z}{}\left({t}\right){+}{\mathrm{ln}}{}\left({z}{}\left({t}\right){+}{1}\right){=}{-}\frac{{{t}}^{{2}}}{{2}}{-}{t}{-}{\mathrm{ln}}{}\left({t}{-}{1}\right){+}{\mathrm{_C1}}$ (2)
 > $\mathrm{ode2}≔\mathrm{diff}\left(y\left(x\right),x,x\right)-\mathrm{diff}\left(y\left(x\right),x\right)-x\mathrm{exp}\left(x\right)=0$
 ${\mathrm{ode2}}{≔}\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right){-}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right){-}{x}{}{{ⅇ}}^{{x}}{=}{0}$ (3)
 > $\mathrm{Solve}\left(\mathrm{ode2},y\left(x\right)\right)$
 ${y}{}\left({x}\right){=}{\mathrm{_C1}}{+}{\mathrm{_C2}}{}{{ⅇ}}^{{x}}{+}\frac{{{ⅇ}}^{{x}}{}\left({{x}}^{{2}}{-}{2}{}{x}{+}{2}\right)}{{2}}$ (4)
 > $\mathrm{ode3}≔\mathrm{diff}\left(y\left(x\right),x,x\right)+\frac{5{\mathrm{diff}\left(y\left(x\right),x\right)}^{2}}{y\left(x\right)}=0$
 ${\mathrm{ode3}}{≔}\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right){+}\frac{{5}{}{\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right)}^{{2}}}{{y}{}\left({x}\right)}{=}{0}$ (5)
 > $\mathrm{Solve}\left(\mathrm{ode3},y\left(x\right)\right)$
 $\left\{{y}{}\left({x}\right){=}{\left({6}{}{{ⅇ}}^{{\mathrm{_C1}}}{}{x}{+}{6}{}{\mathrm{_C2}}\right)}^{{1}}{{6}}}{,}{y}{}\left({x}\right){=}{-}{\left({6}{}{{ⅇ}}^{{\mathrm{_C1}}}{}{x}{+}{6}{}{\mathrm{_C2}}\right)}^{{1}}{{6}}}\right\}$ (6)
 > $\mathrm{ode4}≔{x}^{3}\mathrm{diff}\left(y\left(x\right),x,x,x\right)+3{x}^{2}\mathrm{diff}\left(y\left(x\right),x,x\right)-6x\mathrm{diff}\left(y\left(x\right),x\right)-6y\left(x\right)=0$
 ${\mathrm{ode4}}{≔}{{x}}^{{3}}{}\left(\frac{{{ⅆ}}^{{3}}}{{ⅆ}{{x}}^{{3}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right){+}{3}{}{{x}}^{{2}}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right){-}{6}{}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right){-}{6}{}{y}{}\left({x}\right){=}{0}$ (7)
 > $\mathrm{Solve}\left(\mathrm{ode4},y\left(x\right)\right)$
 ${y}{}\left({x}\right){=}{3}{}{\mathrm{_C2}}{}{{x}}^{{3}}{-}\frac{{\mathrm{_C3}}}{{x}}{-}\frac{{2}{}{\mathrm{_C1}}}{{{x}}^{{2}}}$ (8)

Compatibility

 • The Student[ODEs][Solve] package was introduced in Maple 2021.