# Linear systems diff eq question

• sdusheyko
In summary, the person is asking for help solving the differential equation y'+4y=δ(x), where δ(x) is the Dirac delta function. They clarify that there may be a typo in the post and ask for confirmation on the problem and if there is an initial condition specified. They also mention that they will try to solve it themselves and may come back for help if needed.
sdusheyko
given x(t)=impulse
find y(t)

y(prime)=4y=8x

i am lost

I assume there's a typo in your post and the differential equation is actually y'+4y=8x, so you want to solve

$$y'+4y=\delta(x)$$

where $\delta(x)$ is the Dirac delta function. Is this right? Did the problem specify an initial condition? (Engineers typically assume y(0-)=0.)

vela said:
I assume there's a typo in your post and the differential equation is actually y'+4y=8x, so you want to solve

$$y'+4y=\delta(x)$$

where $\delta(x)$ is the Dirac delta function. Is this right? Did the problem specify an initial condition? (Engineers typically assume y(0-)=0.)

you're right about everything you've said. I'm going to stick my head in a diff eq book and if i get lost i'll probably come back and whine.

thanks

## 1. What is a linear system differential equation?

A linear system differential equation is a type of differential equation that can be expressed in the form of a linear combination of the dependent variable and its derivatives. It involves finding the solution that satisfies the given initial conditions and coefficients.

## 2. What is the difference between a linear and a non-linear system differential equation?

A linear system differential equation has a linear relationship between the dependent variable and its derivatives, whereas a non-linear system differential equation has a non-linear relationship. This means that the coefficients in a linear system are constant, while in a non-linear system they may vary.

## 3. How do you solve a linear system differential equation?

To solve a linear system differential equation, you need to first determine the order of the equation, which is the highest derivative present. Then, using the initial conditions and coefficients, you can use various methods such as separation of variables, substitution, or integrating factors to find the solution.

## 4. What is the significance of solving linear system differential equations?

Linear system differential equations are used to model real-life phenomena in various fields such as physics, engineering, and economics. By solving these equations, we can understand the behavior of these systems and make predictions about their future states.

## 5. Can linear system differential equations have multiple solutions?

Yes, a linear system differential equation can have multiple solutions. This is because the solution depends on the initial conditions and coefficients, and there can be different combinations of these that satisfy the equation. However, the solution will always be unique for a given set of initial conditions and coefficients.

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