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Sep 22nd, 2004, 05:58 PM
#1
Thread Starter
Hyperactive Member
confused on how i'm suppose to prove this DE principal, suppose.. .:Resolved:.
Hello everyone,
I have some notes on the principal of superpostion of solutions for homogenous equations. It sounds comlex but it really isn't. I know how to solve prolems like this but our professor comes out of the blew and says, prove the principal.
Well it says
y'' + p(x)y' + q(x)y = 0; <----equation 1
If y1 and y2 are two solutions of the above equation(1), then
y = c1y1 + c2y2; //where c1 and c2 are constants
is also a solution. And i'm suppose to prove that y = c1y1 + c2y2 is also a solution. She said its really simple. She said all we have to do is take the first derivative and 2nd derivative of y = c1y1+c2y2 and then plug that value into the above equation (1). But this confused because if i take the first derivative of y, i would get:
y' = c1 + c2;
y'' = 0 + 0;
what am i supose to do with that mess? after plugging it into the above equation i get no where. Any idea's on how i am suppoe to prove this?
Thanks!!
Last edited by voidflux; Sep 23rd, 2004 at 07:24 PM.
C¤ry Sanchez
Computer Science/Engineering
@ Penn State
IBM.zSeries Intern
Mandriva 2007
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Sep 23rd, 2004, 01:58 AM
#2
The solutions y1 and y2 are functions, not constants. Therfore, when you take derivatives:
y' = c1y'1 + c2y'2
y'' = c1y''1 + c2y''2
Plug those in along with
y = c1y1 + c2y2
and you're done.
Lottery is a tax on people who are bad at maths
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Sep 23rd, 2004, 09:20 AM
#3
Thread Starter
Hyperactive Member
Thanks again, it worked!
Last edited by voidflux; Sep 23rd, 2004 at 07:24 PM.
C¤ry Sanchez
Computer Science/Engineering
@ Penn State
IBM.zSeries Intern
Mandriva 2007
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