Solving ODEs with Laplace. Stuck at Partial Fraction Expansi

  • #1
193
7

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


81c8a71b26.png

[/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.
 

Answers and Replies

  • #2
LCKurtz
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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##.
 
  • #3
193
7
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##.
436750c918.png


Not sure how to compare these?
 
  • #4
Ray Vickson
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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?
 

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