# Laplace initial value problem> HELP PLEASE

• leenaa
In summary, the Laplace initial value problem is to find a solution for y(0) that satisfies the equation y'(0) = 0. The OP has found a solution for y(0) = 0, but there are an infinite number of solutions that have different values of y'(0).
leenaa
Laplace initial value problem... HELP! PLEASE!

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Hello all!
I'm stuck on this question:

y''(t)+ 4y'(t) = sin2t

y(0) = 0

solve it using laplace transform,... my final is tomorrow, and its 2 am, i would appreciate a quick respone

Last edited:

I can not!

Thank you very much
But I have a problem is all Constants equal to zero!
What reason?

Maybe because your initial condition works out that way? I didn't work your problem.

The problem lies in the
y'(0) = 0
As a result, all the constants equal to zero

If you say so :) Like I said I didn't work your problem.

Thank you
Your participation in the subject to others if allowed

leenaa
this solution is very straightforward so I am not going to solve it for you but I will tell you the steps you should do to get to the final solution. THis is a DE, u need to find y(t).

Step 1)
Find the laplace transforms for y'', y', y... note the LT of y is just Y(s)
Find the laplace transform for the right hand side of the equation.
Apply the initial conditions.

Step 2)
Put it all back in the algebraic equation and solve for Y(s),
Step 3)
find the laplace inverse of Y(s) and that will give you y(t)

good luck, and I hope this is helpful and not to late.

Didn't the OP already say they solved it?

Am I the only one to notice that this is a second order d.e. and there is only one initial condition?

There exist an infinite number of solutions that have different values of y'(0).

y(t)= C- (C+ 1/4)e^{-4t}+ 1/2 cos(t)+ (1/4)sin(2t) satisfies this equation and y'(0)= 0 for any value of C.

In post 7, the OP says y'(0) = 0 which seems to be in addition to y(0) = 0?

## 1. What is the Laplace initial value problem?

The Laplace initial value problem is a mathematical concept in which the solution to a differential equation is determined by specifying both the initial value and the initial derivative of the function. It is often used in physics and engineering to model systems that involve rates of change.

## 2. How is the Laplace initial value problem solved?

The Laplace initial value problem is solved by using Laplace transforms, which convert the differential equation into an algebraic equation that can be solved using inverse Laplace transforms. This method is particularly useful for solving linear differential equations with constant coefficients.

## 3. What are the applications of the Laplace initial value problem?

The Laplace initial value problem has various applications in physics, engineering, and other fields. It is commonly used to analyze circuits, control systems, and heat transfer problems. It can also be used to model population growth, chemical reactions, and other dynamic systems.

## 4. What are the limitations of the Laplace initial value problem?

Although the Laplace initial value problem is a useful tool for solving differential equations, it has some limitations. It can only be used for linear differential equations with constant coefficients, and it may not provide an accurate solution for systems with discontinuous or non-differentiable functions.

## 5. Are there any alternative methods for solving initial value problems?

Yes, there are alternative methods for solving initial value problems, such as the method of undetermined coefficients, variation of parameters, and Euler's method. These methods have their own advantages and limitations, and the choice of method depends on the specific problem at hand.

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