- #1

sandy.bridge

- 798

- 1

## Homework Statement

Having issues determining what I am doing wrong, so perhaps one of you can pin point it. I have the solution, and I am extremely close to the same result, however, I am nonetheless wrong.

Find the conservative vector fields potential.

[tex]\vec{F}(x, y, z)=[(2xy-z^2), 2yz+x^2), y^2-2zx)][/tex]

## The Attempt at a Solution

[tex]\vartheta=\int(2xy-z^2)dx=x^2y-z^2x+C(y, z)[/tex]

then we have

[tex]2yz+x^2=x^2+∂C(y, z)/∂y[/tex]

therefore,

[tex]C(y, z)=zy^2+C(z)[/tex]

It's at the following step that I mess something up.

[tex]y^2-2zx=y^2+∂C(z)/∂z[/tex]

In the solutions however, they have,

[tex]y^2-2zx=y^2-2zx+∂C(z)/∂z[/tex]

However, wouldn't the "-2zx" term go with ∂C(z)/∂z?