A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
y=c1sin x + c2cos x is a solution to y''+y=0.
a. determine whether there are one or more members of this family that satisfy the conditions y(0)=0 and y(pi)=0.
b. Show that the zero function, y(triple bar)0, is the only member of the family that satisfies the conditions y(0)=0 and y(pi/2)=0.
anonymous
 4 years ago
y=c1sin x + c2cos x is a solution to y''+y=0. a. determine whether there are one or more members of this family that satisfy the conditions y(0)=0 and y(pi)=0. b. Show that the zero function, y(triple bar)0, is the only member of the family that satisfies the conditions y(0)=0 and y(pi/2)=0.

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0For a... are you just supposed to substitute the 0 for x, and then the pi for x... b/c then you get 1 and 1, not zero... but what does that tell me?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and for b, Im unsure of what it is really asking me?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1y(0)=c2, not 1 you are trying to find conditions for c1 and c2 that satisfy the conditions

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1y(0)=c2 y(pi)=c2 what requirement does this put on c2 ? what about on c1 ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well if y(0)=c2, then c2 must be equal to 0 right? and I guess it really doesnt matter what c1 is does it?

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.1exactly, so the answer for the first part is that c2=0 and c1 can be any real number. for the next part, what system of equations do you get by plugging in x=0 and x=pi/2 ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0well when x =0 then all you have is y=c2 and if you plug in pi/2 you get y=c1

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.1yes, and we are told that y(0)=0 and y(pi/2)=0, so what are c1 and c2 ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0well then both have to be 0?

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.1yep, so then we just have that y(x)=0 for all x, also known as the zero function http://mathworld.wolfram.com/ZeroFunction.html

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay, thank you. makes sense. but what is the difference between y=0, and y(triplebar)0?

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.1I have never heard of the triple bar notation. I think they are just using it to emphasize that y(x)=c1y2(x)+c2y2(x)=(0)y1+(0)y1=0 as opposed to just having either the c1y1 or c2y2 term =0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0alright.. well thank you again. much appreciated.

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.1it's like a trivial solution vector (c1=0, c2=0, c3=0, ..., cn=0)\[f(x)=\vec 0\]I usually see the triple bar thing used for definitions, but here I suppose it means this. That's all I know :p
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.