numerically approximate the solution to a first order initial value problem using Euler's method - Maple Programming Help

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Student[NumericalAnalysis][EulerTutor] - numerically approximate the solution to a first order initial value problem using Euler's method

 Calling Sequence EulerTutor(ODE, IC, t=b)

Parameters

 ODE - (optional) equation; first order ordinary differential equation of the form $\frac{ⅆ}{ⅆt}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}y\left(t\right)=f\left(t,y\right)$ IC - (optional) equation; initial condition of the form y(a)=c, where a is the left endpoint of the initial-value problem t - (optional) name; the independent variable b - (optional) algebraic; the point for which to solve; the right endpoint of this initial-value problem

Description

 • The EulerTutor command launches a tutor interface that computes and plots the numerical approximation to y(b), the exact solution to the given initial-value problem, using Euler's method.
 • If EulerTutor is called with no arguments, EulerTutor(), it uses a default ordinary differential equation.
 • If IC is not specified, EulerTutor uses a default initial condition.
 • If the t = b argument is not specified, InitialValueProblemTutor uses a default endpoint.
 • The EulerTutor returns either a plot or a value. For information on how to obtain other return values using the Euler command, see Euler.
 • The step-by-step calculations in the EulerTutor are only available from within the tutor interface.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{NumericalAnalysis}}\right):$
 > $\mathrm{EulerTutor}\left(\right)$
 > $\mathrm{EulerTutor}\left(\frac{ⅆ}{ⅆt}y\left(t\right)=y\left(t\right)+t\mathrm{cos}\left(t\right)\right)$
 > $\mathrm{EulerTutor}\left(\frac{ⅆ}{ⅆt}y\left(t\right)=y\left(t\right)+t\mathrm{cos}\left(t\right),y\left(0\right)=0.5\right)$
 > $\mathrm{EulerTutor}\left(\frac{ⅆ}{ⅆt}y\left(t\right)=y\left(t\right)+t\mathrm{cos}\left(t\right),y\left(0\right)=0.5,t=3\right)$