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Math Help - Linearizing ODE

  1. #1
    Senior Member Dinkydoe's Avatar
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    Linearizing ODE

    Im kind of lost on linearizing the ODE y''+\arctan(y)=0

    I should convert this to something like y'=Ay

    I guess with y'=(y',y'') and y=(y,y'). Can someone refresh my memory a little? ;p

    [edit] I found out I have to convert the system into something like this

    x_1=y, x_2=y', x_1'=x_2, x_2'=-\arctan(x_1)
    Last edited by Dinkydoe; April 2nd 2010 at 07:37 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Dinkydoe View Post
    Im kind of lost on linearizing the ODE y''+\arctan(y)=0

    I should convert this to something like y'=Ay

    I guess with y'=(y',y'') and y=(y,y'). Can someone refresh my memory a little? ;p

    [edit] I found out I have to convert the system into something like this

    x_1=y, x_2=y', x_1'=x_2, x_2'=-\arctan(x_1)
    Linearise about where?

    For small y\ \arctan(y)\approx y, so the linearisation would give:

    y''+y=0

    CB
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