# Linearizing ODE

• Apr 2nd 2010, 07:15 AM
Dinkydoe
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

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

$x_1=y, x_2=y', x_1'=x_2, x_2'=-\arctan(x_1)$
• Apr 2nd 2010, 10:30 PM
CaptainBlack
Quote:

Originally Posted by Dinkydoe
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

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

$x_1=y, x_2=y', x_1'=x_2, x_2'=-\arctan(x_1)$

For small $y\ \arctan(y)\approx y$, so the linearisation would give:
$y''+y=0$