differential equation solution for control system

This is my equation

c(t) is output and r(t) input

I want find ;

1) transfer function [C(s)/R(s)]

2) partial-fraction expansion of [C(s)/R(s)

3) the output c(t) and plot step responce system

I am trying to learn matlab for my project but i didnt solving problems.I will be happy if you help

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[William Alberg]

The transfer function can be inserted into matlab the following way:

% make transferfunction
b = 1;
a = [1 5 6 10];
G = tf(b,a);

For partial-fraction expansion, you can use the function "residue". See: https://se.mathworks.com/help/matlab/ref/residue.html

[r,p,k] = residue(b,a);

The step response can be found by using the command "step"

figure;
step(G)