Question

Find an equation for dy/dx if 7=xy-e^xy

Answer 1

Can you differentiate both sides? You might also need some implicit differentiation, or whatever you call it, using the chain rule.

Answer 2

I have this so far \[y+xy'-((y+xy')e ^{xy})=0\]

Answer 3

that looks fine to me. just isolate \(y'\).

Answer 4

That is where I am having trouble. Would it be\[y'=\frac{ -y }{ x-((y+x)e ^{xy}) }\]

Answer 5

To begin, write the expression as\[(y + xy') (1 - e^{xy}) = 0\]If \(x, y \ne 0\), then:\[y + xy' = 0 \Rightarrow y' = - \frac{y}{x}\]