A Applying the Laplace transform to solve Differential equations

[LagrangeEuler]

Is it possible to apply Laplace transform to some equation of finite order, second for instance, and get the differential equation of infinite order?

 

[pasmith]

A laplace transform turns a differential equation into an algebraic equation.

 

[vela]

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.

 

[LagrangeEuler]

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.

 

[hutchphd]

Do you have an example in mind?

 

[LagrangeEuler]

$y''(t)+\sin(t)y(t)=0$, where $y(0)=A$, $y'(0)=B$. If I apply the Laplace transform would I get the differential equation of infinite order?