hi i can't solve this differential equation by ode45 beacause it has sigularity.
xy"=3xcos(x)+sin(x) ; x(0)=0 , x'(0)=0
can you help me to write ode45 function?
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A:
You can use the sinc(x) function, which is defined as sin(π*x)/(π*x), except at x=0 where its value is 1. So, you can rewrite your ODE as:
y'' = 3*cos(x) + sinc(x/π)
which ode45 shouldn't have any trouble solving.
Ray
2010-09-21 23:04:22
Don't you need to throw a `π` in there somewhere? `y'' = 3*cos(x) + π * sinc(x/π)` maybe?
CanSpice
2010-09-21 23:08:15
@CanSpice: You're right; I forgot the factor of π on the outside.
Ray
2010-09-21 23:26:47
Actually, I don't think the factor of π should be there, since `sinc(x/π) = sin(x)/x`, which is the term being replaced.
gnovice
2010-09-22 02:44:21
Okay, so it was right the first time. I can't say I'm a fan of the normalized sinc function, but that's what's implemented in Matlab.
Ray
2010-09-22 04:55:31