understanding the idea behind laplace transform

garimella

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I just want to understand the idea behind Laplace transform. How could the formula be conceived in the form that we know today. Laplace transform is intended to convert linear differential equation to algebraic form. How does this transform apply to non linear differential equations.
 
I just want to understand the idea behind Laplace transform. How could the formula be conceived in the form that we know today. Laplace transform is intended to convert linear differential equation to algebraic form. How does this transform apply to non linear differential equations.

How could the formula be conceived in the form that we know today.

To know that you need to take a class in history of mathematics.

Only certain class of Non-linear DEs can be solved through Laplace transform. Google it - and you'll find many scholarly papers on the subject.
 
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