You can't just take the Laplace transform on one factor! Multiply each term by 12e-3s:fredrick08 said:ok so then F(s)=12e-3s((-6/s)+(4/(s+1))+(2/(s-2)))
=invlaplace(12e-3s)(-6H0(t)+4e-t+2e2t)
then this i think its s-shift or t-shift thing I am not sure about... its something like
H3(t)(-6H0(t-3)+4e-(t-3)+2e2(t-3))
please help, I am not sure with these shifts... i think I am on right track, but it don't look right
A second order Laplace differential equation is a mathematical equation that involves a function and its derivatives with respect to the Laplace transform variable, usually denoted as s. It is a powerful tool in solving problems in engineering, physics, and other scientific fields.
The first step in solving a second order Laplace differential equation is to take the Laplace transform of both sides of the equation. This will convert the differential equation into an algebraic equation, which can then be solved for the function in terms of s. The inverse Laplace transform is then applied to get the solution in terms of the original variable, usually denoted as t.
Solving second order Laplace differential equations is important because it allows us to model and solve complex physical systems and phenomena. It is also a useful tool in control theory, where it is used to analyze and design systems such as electrical circuits and mechanical systems.
There are several techniques that can be used to solve second order Laplace differential equations, such as the method of variation of parameters, the method of undetermined coefficients, and the method of Laplace transforms. Each technique has its own advantages and is useful in different situations.
While Laplace transforms are a powerful tool, they do have some limitations. One limitation is that the initial conditions of the differential equation must be known in order to apply the Laplace transform. Additionally, some differential equations may not have a closed-form solution, making it difficult to solve using Laplace transforms.