Implicit differentiation proof (1 Viewer)

[watatank]

Hi,

Here's to hoping that someone will be able to help out here...even though you are all asleep...

I'm doing Uni level maths at this point in time, but this is a 4 Unit topic so i'm posting here in the hope that you can help me. I'm stuck on an assignment question. This is like major ego points right here, if you can do this question its one less thing you will have to learn in uni...

would you be able to help me show, by implicit differentiation...

(xy-x^2)(dy/dx) = y^2 has a solution of y = Ae^(y/x)

I can differentiate implicitly but I've got no idea how to set out this proof...help would be awesome!

Thanks :wave:

 

[Mill]

It's pretty easy hat.

Take ln of both sides to start with. Call this equation (1).

Multiply through by x.

Differentiate.

Multiply through by y.

Rearrange to have dy/dx on one side.

Multiply through by x so that the dy/dx side of the equation is as required.

Use equation (1) here to fix the other side of the equation.

The end.