# Solving Impulse-Diffy Equation: y''+2y'+3y=sin(t)+δ(t-3π)

• polarbears
In summary, an impulse-diffy equation is a type of differential equation that includes a term for the Dirac delta function, which represents sudden, large changes in a system. It differs from a regular differential equation in that it requires a more complex solution due to the inclusion of the impulse term. The general method for solving an impulse-diffy equation involves using the Laplace transform and its inverse. This equation has various physical interpretations and applications, including analyzing the behavior of systems with sudden changes in fields such as physics, engineering, and biology.
polarbears

## Homework Statement

$$y''+2y'+3y=sin(t)+\delta (t-3 \pi )$$

## The Attempt at a Solution

Left side is just $$Y(s)*(s^2+1)-1$$
But I don't know how to deal with the delta function, I made it into just an intergral but I don't know how to intergrate it.

$$L[\delta(t-t_0)]=e^{-t_0 s}$$

If I remember correctly that is.

thanks=)

## 1. What is an impulse-diffy equation?

An impulse-diffy equation is a type of differential equation that includes a term representing a Dirac delta function. This function, denoted as δ(t), is a mathematical tool used to model sudden, large changes in a system.

## 2. How is an impulse-diffy equation different from a regular differential equation?

An impulse-diffy equation differs from a regular differential equation in that it includes a term for the Dirac delta function, which represents a sudden, large change in the system. This makes the solution to the equation more complex, as it must account for the effects of the impulse.

## 3. How do you solve an impulse-diffy equation?

The general method for solving an impulse-diffy equation involves taking the Laplace transform of the equation, solving for the Laplace transform of the solution, and then taking the inverse Laplace transform to obtain the solution in the time domain.

## 4. What is the physical interpretation of an impulse-diffy equation?

An impulse-diffy equation can be used to model physical systems with sudden, large changes. For example, it can be used to analyze the motion of a mass-spring system when a sudden external force is applied, or the electrical response of a circuit when a sudden voltage is introduced.

## 5. What are some applications of solving impulse-diffy equations?

Impulse-diffy equations have various applications in physics, engineering, and other fields. They can be used to analyze the behavior of systems with sudden changes, such as in control systems, signal processing, and circuit analysis. They can also be used in modeling biological systems, such as the response of neurons to stimuli.

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