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Math Help - ode uniqueness #2

  1. #1
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    ode uniqueness #2

    Show that if g and g' are cont. on R and f is cont. on R, then the solution y(t,o,A,B) of

    y''+ f(y) y'+ g(y)=0 , y(o)=A, y'(o)=B

    exists locally, is unique and can be continued so long as y and y' remain bounded.

    Hint: (Use a transformation)
    Last edited by mr fantastic; October 18th 2010 at 04:04 PM. Reason: Edited title.
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  2. #2
    Super Member Rebesques's Avatar
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    Quote Originally Posted by Fibonacci88 View Post
    Show that if g and g' are cont. on R and f is cont. on R, then the solution y(t,o,A,B) of

    y''+ f(y) y'+ g(y)=0 , y(o)=A, y'(o)=B

    exists locally, is unique and can be continued so long as y and y' remain bounded.

    Hint: (Use a transformation)

    A direct application of the known theorem concerning the dependence of autonomous de's on initial data.
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