Question

Determine whether the equation is separable or not. Write separable ones in separable
form. Determine constant solutions, if any.
y'=1+y

Answer 1

It is

Answer 2

To write it separable, you just write \(y' = \dfrac{dy}{dx}\) then let y in the left hand side and x in the right hand side

Answer 3

knock knock!! do you get me??

Answer 4

who's there? :o

Answer 5

not really

Answer 6

@zepdrix , Honorary Professor of Mathematics, help pleaaaaaasssse.

Answer 7

\[\Large\rm \frac{dy}{dx}=(1+y)\]"Multiply" dx to the other side,\[\Large\rm dy=(1+y)dx\]So from here, how do we get all the y stuff to one side?
Hmmm.

Answer 8

What do you think cash mony?

Answer 9

integrate?

Answer 10

No, you can't integrate (1+y) against dx.

Answer 11

subtract y?

Answer 12

divide (1+y)

Answer 13

yes, divide the (1+y) to the other side.

Answer 14

\[\Large\rm \frac{dy}{1+y}=dx\]Now you have your x's and y's separated.
You can integrate at this point.

Answer 15

is it \[\ln \left| 1+y \right|\]

Answer 16

how to you integrate? @zepdrix

Answer 17

\[\Large\rm \int\limits \frac{dy}{1+y}=\int\limits dx\]Yes.
\[\Large\rm \ln|1+y|=x+c\]

Answer 18

is that the answer?

Answer 19

Determine `constant` solutions?
Hmm.

Answer 20

`Constant` solutions you can equate to `equilibrium` solutions.
So this occurs when the first derivative is zero.\[\Large\rm y'=1+y\]\[\Large\rm 0~=1+y\]Solve for y.
Does this y value work in our solution that we found?\[\Large\rm \ln|1+y|=x+c\]

Answer 21

y would be -1