( left(e^y+1 ight)^2 e^-y d x+left(e^x+1 ight)^3 e^-x d y=0...

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Transcript

00:01 Alright so given the equation, let's first write that out.

00:19 So we want to separate our function to get everything with a y on one side and everything with an x on the other side.

00:25 So let's separate these two.

00:28 So now we're going to divide both terms on the left side and right side to get everything with a y on the right and everything with an x to the left.

00:52 So we're going to have 1 over e to the x plus 1 cubed e to the negative x dx and then negative 1 e to the y plus 1 squared e to the negative y dy and then we can rewrite this as e to the x over e to the x plus 1 cubed dx equal to negative e to the y e to the y plus 1 squared dy.

01:42 So now we want to integrate both sides.

01:45 So let's do each side individually.

01:48 So let's do the u's up here.

01:50 I have e to the x plus 1.

01:52 So du is e to the x dx.

01:57 So we'll end up with this being 1 over u cubed du.

02:07 So that's just u to the negative 3 du.

02:14 So when we integrate that we just add 1 so this would be u to negative 2 over negative 2.

02:26 So this becomes just e to the x plus 1 squared over negative 2.

02:36 Then let's do the same thing with the right side.

02:42 E to the y plus 1 du is e to the y dy...

Question

( left(e^{y}+1 ight)^{2} e^{-y} d x+left(e^{x}+1 ight)^{3} e^{-x} d y=0 )

Question

( left(e^{y}+1 ight)^{2} e^{-y} d x+left(e^{x}+1 ight)^{3} e^{-x} d y=0 )

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