Question

I don't get this variation of parameters question

Answer 1

\[y''-2y'+y=e^{2x}\]
\[y_c=c_1e^x+c_2xe^x\]

Answer 2

@satellite73

Answer 3

@abb0t

Answer 4

Are you being asked to find the general or partiular solution?

Answer 5

I think \[y=y_c+y_p\] eventually
I guess I'm having trouble figuring out the second derivative to get y_p

Answer 6

Omg. Lol. i didn't see the question. Lol

Answer 7

I get the first derivative..(see attachment)
but then it says set something to zero to get the second derivative

Answer 8

Use wronskian.

Answer 9

Remember:
\[W|y_1, y_2| (x) = y_1(x)y'_2(x)-y_2(x)y'_1(x)\]

Answer 10

so why did they set something to zero?

Answer 11

ohhh...that's just a rule I guess...right?

Answer 12

Idk i forgot. Lol. Im trying to remember.

Answer 13

seems right