Initial-Value Problem with Graph : Laplace Tranformations and Partial Fractions

For t>0, let F(t) be the Phi-periodic function which on [0,pi] has the graph attached to this problem. a) Solve the IVP y"+4y=F(t) y(0)=0=y'(0) b) Graph the solution on the interval [0,3pi] c) Discuss the behavoir of the solution in relation to the equation. For the solution please use Laplace transformations and partia ...continues

Initial value problem//Involving Laplace transformatins and partial fractions

a) Solve the Initial value Problem: y"+y=dπ(t)+d2π(t)+d3π(t)+......dnπ(t) ******dπ.- meaning delta sub index phi******** b) Graph the solution on the interval [0,3π] c) Discuss the behaviour of the solution in relation to the equation. I am looking for a solution for this problem. I need the ...continues

Initial-Value Problem involving Graph, Lapace Transformations and Partial Fractions

Solve the Initial Value Problem where g(t) is the function graphed and it is attached to this problem. Solve the following differential equation: y"-3y'+2y=g(t) y(0)=1 y'(0)=0

Initial-Value Problem : Solve with Laplace Transformations

Using Laplace transformations solve the Initial Value Prblem: y"-2y'+10y=1 y(0)=1 y'(0)=2 For the solution please use laplace transformations and partial fractions.

Laplace transformations

I am looking for the solution of this transformation I need a detailed solution. Also I would like to see the original formula for the Laplace transformations needed. If f(t) is a periodic, continuous function with period T>0, show that its Laplace transform is... Please see attached.

Isotope half-life

I am looking for the solution for this problem. Please show all assumptions, set up, and a detailed solution. I need set up, solving the equation and the final amount of material at any time. A certain isotope has a half-life of 5 years. A sample of the isotope has... Please see attached.

Differential equation and spring

I am looking for a detailed solution. I need set up, solving, and final result. Therefore, I need solution of the second order DFQ. Finally for the description of the movement as time goes to infinity, I need what type of motion is that. a. An 8lb weight is attached to a spring suspended from the ceiling. When the weight come ...continues

Initial value problem

Solve the initial value problem... Please see attached.

Existence and uniqueness of solution

I just need to know in a simple statement for each problem if the solution exists, if it is unique, and what is the interval. Based on what is unique?

Initial Value Problem

I am looking for the solution of this problem. It involves a little bit of theory in the second part. In the solution give a detailed solution showing all assumptions and theorems.