Plotting a solution to a differential equation

sm311o_1.mws,wdj,1-9-98

> with(plots):

The first method is to explicitly solve the DE and then plot the function. Obviously, this will not work if MAPLE cannot solve the DE explicitly.

> de:=diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=0;
The differential equation

> ic:=D(y)(0)=0,y(0)=1;
The initial conditions

> soln:=dsolve({de,ic},y(x),method=laplace);
The DE and IC need to be surrounded by curly brackets. The option method=laplace insures that the solution function will probably be expressed in the same form as if you solved it yourself by hand.

> y0:=t->subs(x=t,rhs(soln)):
y0(x);
You have to (unfortunately) create a function - called y0 to distinguish it from the dependent variable y - in MAPLE from the solution soln using the arrow notation -> and the substitution command subs . This is because MAPLE does not recognize the right hand side of the solution rhs(soln) as a function but sees it as a sequence of symbols.

> plot(y0(x),x=0..1);

The second method to plot the solution to a DE in MAPLE involves the plotting command odeplot . This method works even if MAPLE cannot solve the DE explicitly.

> numsoln:=dsolve({de,ic},y(x),type=numeric);

> odeplot(numsoln,[x,y(x)],0..1);

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