Problem involving second order DFQ

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 IVP... Please see attached.

Existance 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?

First order DFQ W/Initial Value

I am looking ofr 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 assuptions and theorems.

Explicit Euler Method

Was Euler the ancient fortune-teller? He almost was. One of his principles, the explicit method says that your future days could be predicted from your present day knowing your past provided your time frame is not too large. Have a look at the solution to a system of non-linear differential equations system using explicit or ...continues

Circular motion of a car

A model racing car of mass 0.2 kg is attached to a model string of length 10m. The car is moving anti clockwise ... See attached file for full problem description.

Solving a homogeneous differential equation

(See attached file for full problem description)

Solving 2 ODE's with one unknown/algebra

Please see attachment, and use equation editor as I did so there is no confusion in your solution. Thank you! --- (See attached file for full problem description)

Differential equations, The Contraction Mapping Theorem

1). Define T : C[0,1] --> C[,1] by (Tx)(t) = 1 + integral from 0 to 1 x(s)ds. Is T a contraction? ( Please justify every step and claim, I want a proof not a yes or no only). P. S. I believe C[0,1] is the set of all the continuous functions on [0,1]. 2). Consider the operator in C[0,1], Ty(t) = integral from 0 to t (t-s)* ...continues

Set of functions defined on [0,1] that have a continuous derivative there ( one-sided derivatives at the endpoints).

A). Let M be the set of functions defined on [0,1] that have a continuous derivative there ( one-sided derivatives at the endpoints). Let p(x,y) = max_[0,1]|x'(t) - y'(t)|. 1).Show that ( M,p) fails to be a metric space. 2). Let p(x,y) = |x(0) - y(0)| + max_[0,1]|x'(t) - y'(t)|. Is (M,p) now a metric space? Please ...continues