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**# (Anything after `#' is for comments. Maple does not treat them as input.) This is a tutorial to some common commands on solving differential equations.**

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**with(plots): # Load up the graphic package. End any command with `:' if you don't want to see the output. Otherwise, end it with `;'. **

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**with(DEtools): # Load up another package for differential equations.**

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**?dsolve; **

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**# Asking question in the form ``?[subject]'' is a very useful tool to learn new commands and techniques. **

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**ode:=diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=cos(t);**

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**dsolve(ode,y(t));**

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**ic:=y(0)=10,D(y)(0)=-1;**

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**solu:=dsolve({ode,ic},y(t),type=numeric):**

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**a:=odeplot(solu,[t,y(t)],0..10,color=black):**

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**display({a});**

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**?dfieldplot; # Find out how to plot direction field.**

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**dfieldplot(diff(y(t),t)=y(t)*(1-y(t)),y(t),t=-3..3,y=-3..3,\
title=`Logistic Equation`);# You can assign variable colors using an expression such as `color=1/2*(-t-(t^2+4*y)))'.**

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**phaseportrait([D(x)(t)=-x(t)-y(t),D(y)(t)=2*x(t)-y(t)], \
[x(t),y(t)],t=0..20,[[x(0)=1,y(0)=0],[x(0)=3,y(0)=3]],x=-4..4,y=-4..4,stepsize=.05, \
scene=[x(t),y(t)],linecolour=sin(t*Pi/2)); # Here is another way to do vector field with solutions.**

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