A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Verify that the given functions form a basis for the space of solutions of the given differential equation. y"+y=0, f1(x)=cosx, f2(x)=sinx
anonymous
 5 years ago
Verify that the given functions form a basis for the space of solutions of the given differential equation. y"+y=0, f1(x)=cosx, f2(x)=sinx

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first do u know what sin and cos is ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol kind of juss started learing it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok sin is o/h and cos is a/h

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1Every second order linear homogeneous equation with linear coefficients \[ y'' + ay' + by = 0 \] has a two dimensional solution space. That is, there exist two linearly independent solutions to the equation. If we call them y_1 and y_2, then the general solution of the equation is \[ y = c_1y_1 + c_2y_2 \] Hence, for your problem, it is sufficient to show that 1. cos x and sin x are solutions of the differential equation; and 2. cos x and sin x are linearly independent You can show number 1 by just showing cos x and sin x satisfy the differential equation. Number 2 I leave to you.
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.