- #1

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## Homework Statement

(28y

^{6}- 24e

^{-6y})(sqrt(1-t

^{4}))dy -(10t)dt =0

Come up with a solution to this equation in the form of a function F(t,y)=0.

## Homework Equations

dF/ dy = N

dF / dt = M

Note: when I write d it's supposed to be a partial derivative.

## The Attempt at a Solution

Okay, so I called the part in front of the dy 'N' and the part in front of the dt 'M'. Then I took dM/dy and dN/dt to make sure they're equal. They are, so this equation is exact.

F(t,y) = integral of (-10t)dt = -5t

^{2}+ k(y)

Now, take the partial derivative of F(t,y) with respect to y. This gives -5t

^{2}y + k`(y). This equal to N.

So -5t

^{2}y + k`(y) = (28y

^{6}- 24e

^{-6y})(sqrt(1-t

^{4}))

There's where I get stuck. I need to figure out what k(y) is, but I have nooo idea how to do that. I tried moving everything over to the right side except k`(y) and integrating, but the integral got really complicated =\