1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Equations

  1. Aug 6, 2006 #1
    Hi, I am finding some of this confusing, can someone explain this?

    so I undersand that [tex]xy' + y = (xy)'[/tex]

    lets say that I have [tex]2ty' + 4y = 2t^3[/tex], what is (xy)'?

    would it just become [tex]d/dx(2ty) = 2t^3[/tex]?
     
    Last edited: Aug 6, 2006
  2. jcsd
  3. Aug 6, 2006 #2

    StatusX

    User Avatar
    Homework Helper

    You're mixing up x and t. If you just want to solve:

    [tex]2t \frac{dy}{dt}+4y=2t^3[/tex]

    then you should use integrating factors. That is, find a pair of functions f(t) and g(t) such that (substituting back y' for dy/dt):

    [tex]f(t) (2t y'+4y)= \frac{d}{dt} (g(t) y)[/tex]

    Right away you can see that 2tf(t)=g(t), and then you can get a simple ODE to solve for g(t). Now you multiply across in the original equation:

    [tex]f(t) (2t y' +4y)=\frac{d}{dt} (g(t) y)=f(t) 2t^3[/tex]

    and then you just need to integrate. Note that the case (xy)' you describe first is another example of integrating factors, in that case with g(x)=x. In this case, g will be different.
     
    Last edited: Aug 6, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear Equations
  1. Linear Equation (Replies: 4)

  2. Linear Equations (Replies: 8)

  3. Linear Equations (Replies: 2)

  4. Linear Equations (Replies: 2)

  5. Linear equation (Replies: 3)

Loading...