Question

I need help with seperable equations

Answer 1

\[y \prime = 6(1+x)^6\]

Answer 2

I'm really confused by these types of problems. I'm new to diffy Q

Answer 3

\[\large \frac{dy}{dx}=6(1+x)^6\]We'll start by moving the dx to the other side.
Simply think of this process as multiplication for now :) No reason to confuse yourself.\[\large dy=6(1+x)^6 \;dx\]We'll take the integral of both sides,\[\large \int\limits dy=\int\limits 6(1+x)^6 \;dx\]Understand up to this point? :D

Answer 4

yes this is where I get lost

Answer 5

So the left side should be fairly straight forward.
The anti-derivative of a constant is the variable we're integrating with respect to.\[\large y+c=\int\limits 6(1+x)^6 \;dx\]

Answer 6

right no do I just differentiate this like usual?

Answer 7

anti-differentiate it like usual, yes :)
Since the inner function is 1+x, we don't need to worry about the chain rule causing trouble for us on this one.

We can simply apply the `Power Rule for Integration` and get a nice clean answer.

Answer 8

So you're new to Diff EQ, but have you had some work with Integrals yet? :D I hope hehe

Answer 9

haha @zepdrix diff eq is like cal 4 in my college, so i would hope they have at least passed cal 2 to be in diff eq

Answer 10

XD

Answer 11

yes I have I'm just really confused by how this question is worded let me try to show you

Answer 12

Its set up in parts and the 1st part is

\[\int\limits_{?}^{?} blank dy = black +C \]

Answer 13

black should be blank

Answer 14

and in your solution I dont see dy on the left side...

Answer 15

why did you type blank? I don't understand D:

Answer 16

So it looks like this?\[\large \int\limits \qquad dy= \qquad +C\]

Answer 17

You don't see the dy in mine? Is the equation not showing up correctly?

Or you mean when I came up with the solution part?
The `dy` and the `swirly S bar` both disappear through the process of taking the anti-derivative of the contents of the integral.