Is there a way to make the first part of this look like the second picture depicted here? Also after intigration is there a way to make the highlighted posrtion not have an "ln(e)" parts and just have the exponetials and there constants?

Obviously I dont want to have to manually input this section everytime, is there some command I can use to achieve this goal?

Above is the outcome I am getting at the current time... and I used map(expand,...) to do the expansion then simplifing it goes back to the origional. 

Below is the outcome I would like to achieve...you can see that this is a different method. The problem I have is this is the right click method of expansion and I am tring to build a program that solves matrix ODE's by just inputing the initial matrix and it doing everything so i can check my answers step by step. 

So my question is, is there another method of command input to get the bottom line in the below picture?

convert(Matrix(2, 2, {(1, 1) = (s-2)/(s^2-s-12), (1, 2) = -5/(s^2-s-12), (2, 1) = -2/(s^2-s-12), (2, 2) = (s+1)/(s^2-s-12)}), parfrac);
%;
Error, (in convert/parfrac) input must be a rational polynomial in s

gives me that error and i assume I can not use this command for matrix opperations if that is true is there a way to do it such as issolateing each element and doing each individually and putting it back into a matrix is that posible if so can someone show me the code for that?

Trying to get this function to work in Maple 18 

CharacteristicPolynomial(M,x)

I am trying to creat a way to solve matrix differential equations step by step.

sin(xy) = x + y

subs( y(x)=y, solve( diff(subs( y=y(x), (1) ),x), diff(y(x),x) ) );

-1

subs( x(xy)=x, solve( diff(subs( x=x(xy), (1) ),xy), diff(x(xy),xy) ) );

cos(xy)

I can not get this answer to come out correctly when using this software please help. the correct answer in the back of the book is 

1- y cos(xy)

--------------

x cos(xy) - 1

And is there a way that this program can tutor me on how to get this answer intead of spitting out the answer 

the diff tutor only allows for a one sided equation to be entered.