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Solution via Context Panel

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Controldrag the differential equation.
Press the Enter key.

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Context Panel:
Add an Initial Condition≻$y\left(1\right)\=2$
(See Figure 5.6.3(b).)

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Context Panel: Solve DE≻$y\left(x\right)$

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Context Panel: Righthand Side

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Context Panel: Plot Builder≻2D plot
Set $3\le x\le 3$
view: axis[2]≻$\left[0\,2.5\right]$
2D Options: scaling≻constrained

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Figure 5.6.3(b) "Add Condition" dialog




$x2y\sqrt{1plus;{x}^{2}}\cdot y\prime equals;0$
${x}{}{2}{}{y}{}\left({x}\right){}\sqrt{{{x}}^{{2}}{\+}{1}}{}\left(\frac{{\ⅆ}}{{\ⅆ}{x}}{}{y}{}\left({x}\right)\right){\=}{0}$
$\stackrel{\text{add initial condition}}{\to}$
${x}{}{2}{}{y}{}\left({x}\right){}\sqrt{{{x}}^{{2}}{\+}{1}}{}\left(\frac{{\ⅆ}}{{\ⅆ}{x}}{}{y}{}\left({x}\right)\right){\=}{0}{\,}{y}{}\left({1}\right){\=}{2}$
$\stackrel{\text{solve DE}}{\to}$
${y}{}\left({x}\right){\=}\sqrt{\sqrt{{{x}}^{{2}}{\+}{1}}{\+}{4}{}\sqrt{{2}}}$
$\stackrel{\text{right hand side}}{\to}$
$\sqrt{\sqrt{{{x}}^{{2}}{\+}{1}}{\+}{4}{}\sqrt{{2}}}$
$\to$



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Solution via the ODE Analyzer Assistant

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Controldrag the differential equation.
Context Panel: Solve DE Interactively


$x2y\sqrt{1plus;{x}^{2}}\cdot y\prime equals;0$$\stackrel{\text{solve DE interactively}}{\to}$

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The first pane of the
assistant is shown in Figure 5.6.8. The Context Panel automatically inserts the differential equation into the Assistant.

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To add the initial condition, click the Edit button at the bottom of the "Conditions" window.

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Figure 5.6.3(d) shows the Edit Conditions pane. Fill in the data under "Add Condition", then click both the Add and the Done buttons.

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Press the "Solve Symbolically" button to obtain the "Solve Symbolically" pane shown in Figure 5.6.3(f). Click the Solve button to obtain the analytic solution of the IVP.



Figure 5.6.3(c) Pane 1, ODE Analyzer Assistant





Figure 5.6.3(d) EditConditions pane




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Figure 5.6.3(e) shows the Plot Options pane, launched by clicking the Plot Options button in the Solve Symbolically pane. Change the default values for the range of the independent variable.

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Press the Plot button in the Solve Symbolically pane to obtain a graph of the solution.



Figure 5.6.3(e) Plot Options pane





Figure 5.6.3(f) Solve Symbolically pane






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Note the "Show Maple commands" checkbox with which the dsolve and plot commands used by the assistant can be seen. The "On Quit, Return" dropdown can be used to select what will be returned to the worksheet when the Quit button is pressed. The graph, the analytic solution, the Maple commands, or nothing, can be thereby returned.${}$
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Solution via the dsolve command

$\mathrm{dsolve}\left(\left\{x2y\sqrt{1plus;{x}^{2}}\cdot y\prime equals;0comma;y\left(1\right)equals;2\right\}comma;y\left(x\right)\right)$
${y}{}\left({x}\right){\=}\sqrt{\sqrt{{{x}}^{{2}}{\+}{1}}{\+}{4}{}\sqrt{{2}}}$



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To graph the solution returned by the dsolve command, just the righthand side of the equation $y\left(x\right)\=\dots$is given to the plot command or to the Context Panel's Plots option. For this, the rhs (righthand side) command, or the Context Panel's "Righthand Side" option can be used.
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