Determine the line of force to F and if it's conservative.

[MechanicalBrank]

Homework Statement

F(x,y) =(x²y,xy²)

Homework Equations

The Attempt at a Solution

I wrote the function as a differential equation dy/x²y = dx/xy². After integration I got C+y²=x². This gave me that the line of force is a hyperbolic paraboloid. The function is not conservative. ∂F1/∂y = x² , ∂F2/∂x = y² ⇒ ∂F1/∂y ≠ ∂F2/∂x

 

[HallsofIvy]

Homework Statement

F(x,y) =(x²y,xy²)

The "problem statement" is a single function? What is F? Is it a vector force function? What are you asked to do? Please tell us what the question really is!

Homework Equations

[/B]

The Attempt at a Solution

I wrote the function as a differential equation dy/x²y = dx/xy². After integration I got C+y²=x². This gave me that the line of force is a hyperbolic paraboloid. The function is not conservative. ∂F1/∂y = x² , ∂F2/∂x = y² ⇒ ∂F1/∂y ≠ ∂F2/∂x

 

[MechanicalBrank]

The "problem statement" is a single function? What is F? Is it a vector force function? What are you asked to do? Please tell us what the question really is!

Silly me. Determine the line of force to the function F and if the function is conservative or not.

 

[AfterSunShine]

But what you wrote is not a function.

 

[MechanicalBrank]

Sorry, didn't notice I wrote function, it's supposed to be vector field. I solved it anyhow so it's all good.