Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Jason21

Please Explain about the basis for the space of functions that satify (a) y' - 2y =0, (b) y' - y/x=0? its question number 33 in section 3.5

  • one year ago
  • one year ago

  • This Question is Open
  1. MichaelT
    Best Response
    You've already chosen the best response.
    Medals 0

    (a) the exponential function \[y=e^{2x}\] happens to solve \[y'-2y=0\] and since it's a first order differential equation, all other solutions are multiples of it, i.e. \[c e^{2x} \]. (b) the simple function \[y=x\] solves this equation. and similarly, all solutions are its multiples.

    • one year ago
  2. uwipostgrad2b
    Best Response
    You've already chosen the best response.
    Medals 0

    y'-2y =0 To sole this equation one can write the characteristic equation to get the eigenvalues. Then using each specific eigenvalue, we get unique eigenvectors for each specific one. Now these eigenvalues, together with their vectors form a basis or SOLUTION SET for the equation meaning all other solutions of the equation are simply multiples of the answers found. Suffice to say, the eigenvalues, together with their eigenvectors are linearly independent and so span R^2. Note that the nature of the eigenvalues have a say in the general solution: whether complex, real, and also if we have repeated roots, etc... *** I hope this is sufficient enough to make you want to solve the problem as it is in the doing that we learn. To learn mathematics, one must write and write and write... indeed learning math is simply hard work and we must desire to get our hands dirty.

    • one year ago
  3. uwipostgrad2b
    Best Response
    You've already chosen the best response.
    Medals 0

    actually the solution is as above... i just gave you the method to solve those equations of 2nd order... i felt compelled to tell you.

    • one year ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.