Question

I'm having trouble understanding step/equation 8

Answer 1

it follows from step/equation 7.

Answer 2

since they are solutions, they must = 0

Answer 3

It's the explanation/ derivation of the method of Variation of Parameters. How are y_1 and y_2 solutions of the complimentary equation

Answer 4

I believe that y_1 is, but why y_2?

Answer 5

why not ?

Answer 6

aren't they BOTH assumed/derived to be solution for CE ?

Answer 7

sorry my internet is soo slow, or it could be the website....anyhow I'm back. Let's see....

Answer 8

oh I thought that \[y(x)=c_1y_1(x)+c_2+y_2(x)\]

meant:
y(x)= complimentary equation + particular solution

Answer 9

sorry typo
y(x)=c_1y_1(x)+c_2y_2(x)

Answer 10

\[y(x)=c_1y_1(x)+c_2y_2(x)\]

Answer 11

that is just the complimentary soln.

Answer 12

do you want me to attach the whole page?

Answer 13

oh ok

Answer 14

I guess the fact that they wrote it as y(x) (instead of y_c) confused me