(28y6 - 24e-6y)(sqrt(1-t4))dy -(10t)dt =0
Come up with a solution to this equation in the form of a function F(t,y)=0.
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 = -5t2 + k(y)
Now, take the partial derivative of F(t,y) with respect to y. This gives -5t2y + k`(y). This equal to N.
So -5t2y + k`(y) = (28y6 - 24e-6y)(sqrt(1-t4))
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 =\