Problem involving diff eq'ns

A mass 5kg is attached to a spring suspended from the ceiling. When the mass comes to rest at equilibrium, the spring has been stretched 2m. The mass... Determine the motion of the mass. Decribe its motion in as much detail as possible. Please see attached.

Initial Value Problem

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

Best statements about solutions

I am looking for the best statements about solutions and how is the statement supported... Please see attached.

Second order Diferential equation with Wronskian

Let y1, y2 be twice differentiable functions on an interval (a,b) whose Wronskian is nowhere zero. Show that there... Please see attached.

Initial value problem with graph condition/Laplace tranformations

For t>0, let F(t) be the Phi-periodic function which on [0,π] 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 [0,3π] c) Discuss the behavoir 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.