A Property of an Autonomous ODE

  • #1
Hi!

I wonder how to prove that if y(t)=sin(t) solves an autonomous ODE f(y,y',...,y^(n))=0, then x(t)=cos(t) is also a solution.

I mean I'm a bit distracted by the fact that all derivatives of y are present here. For example in the equation for a pendulum there are just y and y'' and a special functional dependence between them and that's why it works, isn't it?

In the above case I know almost nothing about the function f. So how to proceed?
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
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Maybe you can use that cos(x) = sin(x + pi / 2)?
 

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