Confused on a first order seperable diff EQ wee

[mr_coffee]

Hello everyone. I'm going back to all my old webworks and trying to finish them and I'm still having problems on first order. It says this is seperable but I'm not seeing it.
Here are the directions:
The differential equation
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/34/514d5bb475169a72ecc1cc497078721.png
has an implicit general solution of the form F(x,y) = K.

In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form
F(x,y) = G(x) + H(y) =K.


Find such a solution and then give the related functions requested.
F(x,y) = G(x) + H(y) =

Okay well this is what i attempted, and I'm not seeing how this is seperable.
http://suprfile.com/src/1/51fysb/lastscan.jpg

the very bottom is the answer the Ti-89 pumped out. But i'd like to know how to do it as well. And the form the Ti-89 put out confuses me, if i want the answer in the form of g(x) + h(y) = K would i solve for C1?

 

[HallsofIvy]

What makes you think that equation is separable?

 

[mr_coffee]

urnt, well it says so in the directions:

In fact, because the differential equation is separable...

 

[finchie_88]

I don't know that much about differential equations, so what I'm about to say could be a load of BS, I'm not sure, anyway, can't that equation be written as $\frac{dy}{dx} = (4x+3)(5y+6)$, then can you not simply separate the varibles and then integrate both sides?

Like I said, I don't have any real knowledge of diff equations, but is that what you mean?

 

[mr_coffee]

finchie, u did it hah, it was right!
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/0a/b633d3ce241b65e80f784da84842d81.png
e-mailing u some cash.

 

[finchie_88]

lol, no worries (That was my first ever attempt at solving a diff equation, before I had seen a few examples, but never actually tried one), I wish my maths teachers offered me money each time I got a question right, lol, oh well, I can always dream...

 

[HallsofIvy]

I don't know that much about differential equations, so what I'm about to say could be a load of BS, I'm not sure, anyway, can't that equation be written as $\frac{dy}{dx} = (4x+3)(5y+6)$, then can you not simply separate the varibles and then integrate both sides?

Like I said, I don't have any real knowledge of diff equations, but is that what you mean?

Well done. That is why it is a separable equation!

 

[HallsofIvy]

finchie, u did it hah, it was right!
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/0a/b633d3ce241b65e80f784da84842d81.png
e-mailing u some cash.

No, it isn't. That isn't even an equation.

 

[mr_coffee]

my bad.
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/57/f15a6cea760ce4906a6ec16f9d29451.png http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/0a/b633d3ce241b65e80f784da84842d81.png