Given the y-intercept of this curve means what? Diff EQ

[mr_coffee]

Hello everyone this may be an easy problem, but I'm confused on what they have given me the problem says:

Find f(x) if y = f(x) satisfies
{dy}/{dx} = 32 yx^{15}
and the y-intercept of the curve y = f(x) is 2.
f(x) = ?


But what does that mean that the y intercept is 2? is that an intial condition? if so what is the value of x? if y = 2? or does that mean y(0) = 2? or does it mean y(2) = 0?

Here is my work:
http://img72.imageshack.us/img72/9646/lastscan8sf.jpg


Any help would be great! thanks! :)

 

[HallsofIvy]

You are doing differential equations and you have to ask what "y- intercept" means? Oh, be embarassed!

The "y-intercept" of a graph may mean either the point at which the graph crosses the y-axis or the y value of that point, since, of course, the x-value of any point on the y-axis is 0. Saying "the y-intercept of the curve y = f(x) is 2" is saying that y(0)= 2.

By the way, is there any reason for dividing by 32? It looks to me like the solution would be simpler if you left it on the right side.
(It especially prevents one from mistakenly writing that e^{\frac{ln y}{32}}= \frac{y}{32}!)
Oh, and e^a+b is NOT e^a+ e^b!

 

[mr_coffee]

Thanks for the advice Ivey, But i seemed to still suck it up in a big way. Here is my new work, still somthing isn't working out!


http://img81.imageshack.us/img81/9937/lastscan5rv.jpg



PS: I am ashamed of myself

 

[codyg1985]

Check the math on the x side of the equation when you integrate.

 

[HallsofIvy]

With good reason! Now I feel I have to point out that 32/16 is NOT 9/4!

 

[mr_coffee]

Oh f word, I don't nkow how i didn't notice that. I should have been on that like a hobo on a hamsandwitch.
Perhaps its the large intake of coffee products or pure ignorance hah. thanks guys, it works!
PS: I even showed my professor and he didn't catch the whole 32/16 != 9/4, but then again he probably figured I could do basic math.