Partial fraction expansion of Laplace transform

[CoolDude420]

Homework Statement

Hi,
So I had a pretty long question solving a Linear ODE but now I've gotten stuck at this stage where I can't seem to get it into the right form to carry out partial fraction expansion

Homework Equations

The Attempt at a Solution

[/B]
I'm quite sure that I what I have at the very last line isn't correct. I'm really new to solving ODEs with Laplace. Q and R are the constant things that you put over the fraction when solving with partial fraction expansion.

 

[LCKurtz]

Homework Statement

Hi,
So I had a pretty long question solving a Linear ODE but now I've gotten stuck at this stage where I can't seem to get it into the right form to carry out partial fraction expansion

Homework Equations

The Attempt at a Solution

View attachment 213056
[/B]
I'm quite sure that I what I have at the very last line isn't correct. I'm really new to solving ODEs with Laplace. Q and R are the constant things that you put over the fraction when solving with partial fraction expansion.

You have$$
Y(s)=\frac{A}{s(sB+1)}$$You want to set that equal to its partial fractions like this:$$
\frac{A}{s(sB+1)} = \frac Q s + \frac{R}{sB+1}$$
Add the two fractions on the right and compare numerators with the left to get $Q$ and $R$.

 

[CoolDude420]

You have$$
Y(s)=\frac{A}{s(sB+1)}$$You want to set that equal to its partial fractions like this:$$
\frac{A}{s(sB+1)} = \frac Q s + \frac{R}{sB+1}$$
Add the two fractions on the right and compare numerators with the left to get $Q$ and $R$.

Not sure how to compare these?

 

[Ray Vickson]

View attachment 213075

Not sure how to compare these?

Well, is $Q(sB+1) + Rs$ equal to the constant $A$ for ALL values of $s$? You need to figure out what values of $Q$ and $R$ make that happen. Did you really not see all this done in calculus 101?