Laplace Transform Applied To Differential Equations - An Example

An Example

We want to solve

with initial conditions f(0) = 0 and f′(0)=0.

We note that

and we get

The equation is then equivalent to

We deduce

Now we apply the Laplace inverse transform to get

Read more about this topic:  Laplace Transform Applied To Differential Equations

Famous quotes containing the word example:

    “Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
    —Marcel Proust (1871–1922)