I was given a few 2nd order differential equations, i found the characteristic equation (aka auxiliary equation) but then it asked for fundamental solution. is that the f(x) equation that relates the roots to the 3 possible solutions (2 real roots, 1 double root, complex roots)?

3/24/2008 5:58:42 PM

if so why does it ask me for two of them?

3/24/2008 6:07:06 PM

if you are only dealing with a few DEs, why don't you write them out here so your question makes more sense?

3/24/2008 6:12:42 PM

people actually do their own maple? wtf mate?

3/24/2008 6:19:16 PM

Was advised to avoid posting the exact problem so i used the same range of numbers
3y(x)'' + 49 y(x)' + 322 y(x) = 0


so i got an auxiliary equation of 3r^2 + 68r + 320.
use the quadratic equation to find the roots -6.666 and -16.

so i'd plug them into y(x)=c1 * e^(-6.66x) + c2 * e^(-16x)



so that gets me

Quote :

"(a) Assuming a solution of the form y(x) = exp(rx) leads to a quadratic equation in the variable r that is called the characteristic (or auxiliary) equation of the ODE. Assign the characteristic equation of the above ODE to the name TheCharacteristicEquation. (b) Solve the characteristic equation and assign the two roots to the name TheRoots as a Maple LIST. For example, TheRoots = [-3,7]. "

what i don't understand is what this means:

Quote :

"(c) Assign to the names FundamentalSolution_1 and FundamentalSolution_2 two linearly independend solutions of the given ODE. Assign only the expressions for the solutions and DO NOT include y(x) = ... in your answers. "

i know how to do all of these by hand but i don't think my professer ever mentioned 'fundamental solutions'.

3/24/2008 6:28:30 PM

nvm, its cool i'll just get another 80% on maple for trying, while people who just copy their roommate's get 100.

maple assignments aren't worth their grade % in any math class anyways.

3/24/2008 6:37:36 PM

the problem is maple assignments don't really test your knowledge of the material as much as they test your knowledge of maple.

3/24/2008 6:48:04 PM

^ yeah. to this day i have yet to have the ability to do anything in a maple assignment, yet i rarely get 100%. Always some bullshit about not having a list in a certain order or my answer varies by 0.01% yeah thats close enough i'm not building a space station.

3/24/2008 7:07:05 PM

so you did the whole: assume your solution is y(x) = C*exp(r*x) to get the characteristic equation for r, i.e.:
a*y''(x) + b*y'(x) +c*y(x) = 0
a*r^2 + b*r + c = 0

since it is a quadratic eq. you get two r values, r1 and r2.

therefore you have two "fundamental" solutions:
y1(x) = C1*exp(r1*x) and y2(x) = C2*exp(r2*x)

since it is a linear homogeneous diff. eq., the sum of the solutions is also a solution (which you already realized):
y(x) = y1(x) + y2(x) = C1*exp(r1*x) + C2*exp(r2*x)

but it appears that you only need to enter the two linearly independent solutions as the "fundamental" solutions.

3/24/2008 7:31:37 PM

oh.

see? its shit like that that gets people discouraged on maple.

3/24/2008 7:49:19 PM

Quote :

"people actually do their own maple? wtf mate?"

3/24/2008 8:35:19 PM

have to retake 241 anyways. might as well just try and learn how to use this.

MAYBE... just maybe it might be useful one day. oh wait no it won't.

3/24/2008 11:52:25 PM

yeah it will,i use maple all the time to solve my homework

3/25/2008 6:30:41 AM

i only ever use maple to do the homework that i can do by hand that i don't want to do.

3/25/2008 9:36:54 PM

As much as I dislike Maple on the average, your problem is one of basic terminology. You should know what is meant by "fundamental solutions" this should be in the textbook and also it should have been emphasized in lecture. There are always two fundamental solutions to a 2nd order ODE.

The blame is on you(or your lecturer) not Maple here. Sorry.

3/26/2008 12:42:22 PM