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implicite differentiation, in this case y(x), such that y is a function of x.

I"m working on the separable equations section of my differential equations chapter.

the gradient would be orthogonal.

I haven't learn anything about gradients yet. This is only chapter 9 of stewart's calculus

for y=k/x
I get
ln|y|=ln|-x|+C
What do you think?

is this the integrated form?

yep.
\[\int \frac1ydy=\int-\frac1x dx\]

ok
ln|y|=-ln|x|+C

perfect.

Thank you!