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This paper is a gem in showing the general idea behind the Laplace transform:

Discovering the Laplace Transform in Undergraduate Differential Equations
by Terrance J. Quinn and Sanjay Rai

The key hypothesis is that that solutions to differential equations are combinations of exponential functions. The Laplace transform is a means of extracting the coefficients and exponents (and therefore the free parameters).

Highly recommended!

show/hide this revision's text 2 added 17 characters in body

This paper is a gem in showing the general idea behind the Laplace transform:

Discovering the Laplace Transform in Undergraduate Differential Equations
by Terrance J. Quinn and Sanjay Rai

The key hypothesis is that that solutions to differential equations are combinations of exponential functions. The Laplace transform is a means of extracting the coefficients and exponents (and therefore the free parameters).

Highly recommended!

show/hide this revision's text 1

This paper is a gem in showing the general idea behind the Laplace transform:

Discovering the Laplace Transform in Undergraduate Differential Equations
by Terrance J. Quinn and Sanjay Rai

The key hypothesis is that that solutions to differential equations are combinations of exponential functions. The Laplace transform is a means of extracting the exponents (and therefore the free parameters).

Highly recommended!