- #1
sdusheyko
- 19
- 0
given x(t)=impulse
find y(t)
y(prime)=4y=8x
i am lost
find y(t)
y(prime)=4y=8x
i am lost
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
[tex]y'+4y=\delta(x)[/tex]
where [itex]\delta(x)[/itex] is the Dirac delta function. Is this right? Did the problem specify an initial condition? (Engineers typically assume y(0^{-})=0.)
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.
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.
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.
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.
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.