could someone give me advice? differential equation.

Hi im having problems with the following 2 question and was wondering if somebody could give me some help on how to do it. Im not the best at math so any help/advice/answer would be greatly appreciated. Feel free to move this thread if its in the wrong catagory.

Totster.

1. (a) Solve the following second order linear differential equation

(d^2(

x)/(d)t^2)+ 5(dx/dt) + 4x = 0

subject to the initial condition x(0) = 0 and x˙(0) = 1. What type

of damping does this motion illustrate?

(b) Solve the following second order linear differential equation

(d^2(

x)/(d)t^2)+ x = cos(t)

subject to the initial condition x(0) = 0 and x˙ (0) = 0. What type

of motion do you find?

2. A satellite undergoes an elliptic orbit about the Earth of mass M, with

maximum distance 6R and minimum distance 3R from the Earth’s

centre where R is the radius of the Earth.

(a) Show that the minimum velocity vmin and the maximum velocity

v

max are given by

v

max = 2vmin = 2/3√ GM/R

(b) Show that the eccentricity of the satellite is

e = 1/3.

Thanks