Question

DIFFERENTIAL EQUATIONS
Situation
Describe in your own words the method you would use to find the Laplace transform of the first derivative, that is,. Give 2 examples.

Situacion:

Describa en sus propias palabras el método que usted utilizaría para hallar la transformada de Laplace de la primera derivada, o sea, . De 2 ejemplos.

Answer 1

One of the main uses of the Laplace transform is its role in the solution of differential equations. The utility of the Laplace transform lies in the fact that the transform of the derivative corresponds to multiplication of the transform by s and then the subtraction of function at zero.

Example:

Given an IVP, apply the Laplace transform operator to both sides of the differential equation. This will transform the differential equation into an algebraic equation whose unknown, F(p), is the Laplace transform of the desired solution. Once you solve this algebraic equation for F( p), take the inverse Laplace transform of both sides; the result is the solution to the original IVP.

Example:

Consider the initial value problem:

Now, let

Y = L(y) and applying the transform of derivative ifentity, we get

If you want something else then please tell me.