Need help solving/graphing diff eqs with Maple

PICsmith

Hi everyone, first time poster here. I'm hoping someone who's familiar with Maple can help me solve this problem from Classical Dynamics of Particles and Systems, Thornton/Marion, 5th ed., Chap 2, number 7. I have the solutions manual which contains this problem, and I can get to where they get to, these 2 parametric equations:

[tex]
\ddot{x}=-b \dot{x} \sqrt{ \dot{x}^2+ \dot{y}^2}
[/tex]
[tex]
\ddot{y}=-b \dot{y} \sqrt{ \dot{x}^2+ \dot{y}^2}-g
[/tex]
(in case LaTeX doesn't work:
x'' = -bx' sqrt((x' )^2 + (y' )^2);
y'' = -by' sqrt((x' )^2 + (y' )^2) - g;)
where b is all the constants

Then they say "solving with a computer using given values....we arrive at these nice graphs here" without bothering to say what steps were needed to do so. I've tried to use Maple to solve for x(t) and y(t) and graph them with no success. Here's how far I get:

> restart:with(DEtools):with(plots):
I assign all the constants their values
> b:=(0.8*1.3*0.2)/(2*30);g:=9.8;
I assign both of the diff eqs to variables, and the output (just what i put in, in pretty symbolic form) is correct
> XDD:= diff(x(t),t$2) = -b*diff(x(t),t)*sqrt( (diff(x(t),t))^2 + (diff(y(t),t))^2);
> YDD:= diff(y(t),t$2) = -b*diff(y(t),t)*sqrt( (diff(x(t),t))^2 + (diff(y(t),t))^2)-g;
Then I assign the solution to another variable for each one (with initial conditions):
> SX:=dsolve({XDD,x(0)=-210,D(x)(0)=44.44},x(t));
> SY:=dsolve({YDD,y(0)=80,D(y)(0)=0},y(t));
but the output in both cases is just:
Empty, no errors though. Now if I remove the initial condition for the velocity at t=0, I do get an output, albeit an ugly one, but it doesn't make a graph, not that I expected it to. I tried to plot parametrically:
plot([SX,SY,t=0..4.44],x=-200..-30,y=0..80);

I think my problem is that both equations are in terms of each other, x(t) and y(t), and can't be solved thus with dsolve( ). Any advise would be appreciated, and this not an assigned problem for school for me although it was last year (I never turned in the graph) so I'm posting here in the HW help section. Thanks.

vladimir69

hi
have u tried having a look at the following section in the maple help file
>help
>mathematics
>differential equations
>dsolve
>system
it might prove to be useful in some way

PICsmith

Cool beans, I solved it Thanks for pointing me in the right direction vladimir. For anyone who might have a similar problem for Maple here is the syntax I used:

> restart:with(DEtools):with(plots):b:=(0.8*1.3*0.2)/(2*30);g:=9.8;

sys = {diffeq1, diffeq2, initial conditions...}
> sys:={diff(x(t),t$2) = -b*diff(x(t),t)*sqrt( (diff(x(t),t))^2 + (diff(y(t),t))^2), diff(y(t),t$2) = -b*diff(y(t),t)*sqrt( (diff(x(t),t))^2 + (diff(y(t),t))^2)-g, x(0)=-210,D(x)(0)=44.44,y(0)=80,D(y)(0)=0};

> fcns:=[x(t), y(t)]:

> soln:=dsolve(sys, type=numeric, range=0..4.44);

> odeplot(soln, fcns);