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 solution to be very esplicit for all three parts and explain all assumptions. For the solution please use laplace transformations and partial fractions.

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

Laplace transformations problem with initial value problem

Using Laplace transformations solve the Initial Value Prblem: y"-2y'+10y=1 y(0)=1 y'(0)=2 I am looking for a solution for this problem. I need the solution to be very esplicit for all three parts and explain all assumptions. For the solution please use laplace transformations and partial fractions.

Laplace transfermations

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

Problem involving second order DFQ

I am looking for the solution for thsi problem. Please show all assuptions, set up, and a detail solution. I need set up, solving the eq'n 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.