A Applying the Laplace transform to solve Differential equations

LagrangeEuler
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Is it possible to apply Laplace transform to some equation of finite order, second for instance, and get the differential equation of infinite order?
 
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A laplace transform turns a differential equation into an algebraic equation.
 
If you had a term like ##\sin t\,y##, you could expand ##\sin t## as a series and take the Laplace transform of the result term by term, which would give you a bunch of derivatives of Y(s). I'm not sure why you'd want to do that though or if doing so is valid.
 
pasmith said:
A laplace transform turns a differential equation into an algebraic equation.
It is only in the case when you have a differential equation with constant coefficients.
 
Do you have an example in mind?
 
##y''(t)+\sin(t)y(t)=0##, where ##y(0)=A##, ##y'(0)=B##. If I apply the Laplace transform would I get the differential equation of infinite order?
 

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