Laplace transform using differential equations

In summary, the conversation is about Laplace transform using differential equations and the question of whether Y'(0) can be treated as a constant or if the limit and differentiation can be changed. The response is that Y(0) and Y'(0) are both constants and their derivatives are both zero. The conversation also discusses the value of Y'(0), which is infinity, and whether it can be treated as a constant. The summary concludes that the value of Y'(0) can be treated as a constant.
  • #1
Belgium 12
43
0
Hi members,

Laplace transform using differential equations.(see attached PDF file)

My question d/ds(s^2 y- s Y(0)-Y'(0).)...
Y(t)=sin(sqrt(t)) Y(o)=0
Now Y'= cos(sqrt(t)/2sqrt(t) Y'(0)=infinity

d/ds (Y'(0)=?? can it be treated as a constant or can we change limit and differentiation??I don't think so.
like d/ds (cos(sqrt(t))/2sqrt(t)=0

Thank you
 

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  • #2
Belgium 12 said:
Hi members,

Laplace transform using differential equations.(see attached PDF file)

My question d/ds(s^2 y- s Y(0)-Y'(0).)...
Y(t)=sin(sqrt(t)) Y(o)=0
Now Y'= cos(sqrt(t)/2sqrt(t) Y'(0)=infinity

d/ds (Y'(0)=??
Y(0) and Y'(0) are constants, so their derivatives are both zero.
Belgium 12 said:
can it be treated as a constant or can we change limit and differentiation??I don't think so.
like d/ds (cos(sqrt(t))/2sqrt(t)=0

Thank you
 
  • #3
Hello Mark 44,

If I understand it,Y'(0)=infinity.Here infinity can be treated as a constant.

Thank you
 

1. What is the Laplace transform?

The Laplace transform is a mathematical operation that converts a function from the time domain to the frequency domain. It is commonly used in the study of differential equations and has applications in various fields of science and engineering.

2. How is the Laplace transform used to solve differential equations?

The Laplace transform can be applied to a differential equation to convert it into an algebraic equation in the frequency domain. This makes it easier to solve the equation using algebraic methods, and the solution can then be transformed back to the time domain using the inverse Laplace transform.

3. What are the benefits of using the Laplace transform in solving differential equations?

The Laplace transform simplifies the process of solving differential equations by converting them into algebraic equations, which can be easier to manipulate and solve. It also allows for the analysis of systems in the frequency domain, which can provide valuable insights into their behavior.

4. Are there any limitations to using the Laplace transform?

While the Laplace transform is a powerful tool in solving differential equations, it is not applicable to all types of functions. It can only be used for functions that are of exponential order, meaning that they grow or decay at a certain rate as time goes on.

5. Can the Laplace transform be used for any type of differential equation?

The Laplace transform can be applied to many types of differential equations, including ordinary and partial differential equations. However, it is most commonly used for linear differential equations with constant coefficients.

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