Solving DEs--General

1. Write DE in Operator notation
1a. take Laplace transform
1b. Solve for "unknown"
2. 
3. Partial fraction expansion
4. Write as sum of n terms
5. Break into terms
6. Solve each term
7. Write together
8.
9. (Just for curiosity) look at SS value
10. REJOICE

IVT & FVT

Solving 2nd order DEs with completing the square

-1.9709 -0.0145 + 1.7154i -0.0145 - 1.7154i
-1.9856 -0.0072 + 1.7238i -0.0072 - 1.7238i
-2.0000 0.0000 + 1.7321i 0.0000 - 1.7321i
-2.0142 0.0071 + 1.7403i 0.0071 - 1.7403i
-2.0281 0.0141 + 1.7484i 0.0141 - 1.7484i
-2.0418 0.0209 + 1.7564i 0.0209 - 1.7564i
-2.0554 0.0277 + 1.7644i 0.0277 - 1.7644i
-2.0687 0.0343 + 1.7723i 0.0343 - 1.7723i
-2.0818 0.0409 + 1.7801i 0.0409 - 1.7801i
-2.0947 0.0474 + 1.7878i 0.0474 - 1.7878i
-2.1075 0.0538 + 1.7955i 0.0538 - 1.7955i
-2.1201 0.0600 + 1.8030i 0.0600 - 1.8030i
-2.1325 0.0662 + 1.8106i 0.0662 - 1.8106i
 

»k=0:.1:6
k =
Columns 1 through 7
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000
...........
4.9000 5.0000 5.1000 5.2000 5.3000 5.4000 5.5000
 
Columns 57 through 61
5.6000 5.7000 5.8000 5.9000 6.0000