Question

Solve for y: (y+e^x)/(y+2e^x)=Ce^x.

Answer 1

first step is multply both sides by (y+2e^x)
can you do that ?

Answer 2

Yes, I got y+e^x=Ce^x(y+2e^x)

Answer 3

next, "distribute" the C e^x on the right hand side
i.e. multiply it times each term inside the parens

Answer 4

I got y+e^x=yCe^x+2Ce^2x

Answer 5

Now what?

Answer 6

yes
add -y to both sides
add -2Ce^2x to both sides

(i.e. get all the terms with y on one side, and the other terms on the other side)

Answer 7

So I got e^x+2Ce^2x=yCe^x+y

Answer 8

you did something wrong.
if (for example) you add -y to both sides:
y+e^x=yCe^x+2Ce^2x
y - y + e^x = yCe^x -y + 2Ce^2x
which simplifies to
e^x = yCe^x -y + 2Ce^2x

notice you have -y on the left side

Answer 9

Now what?

Answer 10

what do you have so far?

Answer 11

e^x=yCe^x-y+2Ce^2x

Answer 12

add -2Ce^2x to both sides (this makes all the terms on the left have a "y" in them)

Answer 13

So I got e^x-2Ce^2x=yCe^x-y

Answer 14

yes, much better.

notice you have a y in both terms on the left side.
any ideas how to "get at it" ?

Answer 15

factor?

Answer 16

yes

Answer 17

Let me try

Answer 18

it's like "undoing" distribute.

Answer 19

Thank you so much, I got the right answer.

Answer 20

yw