interactive symbolic and numeric solution of ordinary differential equations - Maple Programming Help

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dsolve[interactive] - interactive symbolic and numeric solution of ordinary differential equations

 Calling Sequence dsolve[interactive]($\mathrm{odesys}$, options)

Parameters

 odesys - (optional); single ODE, or set/list of ODE, optionally with initial or boundary conditions options - (optional); equations that control the behavior of the interactive solver

Description

 • The dsolve[interactive](odesys,options) command launches a graphical user interface for the investigation and solution of ODE and ODE systems. Note that this interface is written in Maplets. Generally, you can specify what to return to the Maple session. Options include nothing, the displayed plot, the computed numeric procedure, or the Maple commands needed to produce the solution values and/or the displayed plot. For details, see the worksheet,interactive,dsolveinterface help page.
 • If odesys is not given in the call to dsolve[interactive], then odesys can be entered by using the interface; otherwise, the input equations are examined and used as a starting point for the application (these equations can be changed from within the graphical user interface).

Options

 The following optional arguments control the behavior of dsolve[interactive]().
 • maxplots=integer
 Controls the maximum number of plots (based on the solution) that can be displayed simultaneously. The default is 4, and this parameter can range from 1 to 16.
 • display=value
 Controls the size of the font in the application windows (and as a result, the size of the application windows as well). There are two settings, small (the default value) and large. The small setting can display all windows on a 800x600 resolution display, while the large setting requires at least a 1024x768 resolution display.
 • aliasing=boolean
 Controls whether aliasing is used to reduce the size of a symbolic solution. When set to true, large repeated subexpressions are aliased to percent values, such as $%1$, and $%2$. The percent values are displayed in the solution in place of the corresponding subexpression. The sequence of alias definitions follows the solution.
 By default, aliasing is true. Setting it to false disables this aliasing, possibly resulting in expressions that are too large to display.
 • When dsolve[interactive] is invoked, the current setting of the Digits environment variable is used for all numerical computations. If a higher precision is required, Digits must be set to that precision prior to invoking dsolve[interactive].
 • Important: Before using this command, review the information about the operation of the solver in the worksheet,interactive,dsolveinterface help page.

Examples

Investigating a Symbolic Solution

 > $\mathrm{dsolve}\left[\mathrm{interactive}\right]\left(\mathrm{diff}\left(y\left(x\right),x\right)=a\left[0\right]+a\left[1\right]y\left(x\right)+a\left[2\right]{y\left(x\right)}^{2}\right)$

Investigating a Numerical Solution

 > $\mathrm{dsolve}\left[\mathrm{interactive}\right]\left(\left\{\mathrm{diff}\left(y\left(x\right),x,x\right)-10\left(1-{y\left(x\right)}^{2}\right)\mathrm{diff}\left(y\left(x\right),x\right)+y\left(x\right)=0,y\left(0\right)=2,\mathrm{D}\left(y\right)\left(0\right)=0\right\}\right)$