Solving Exact Differential: x(dy/dx) = 2xe^x - y + 6x^2

[illidari]

Homework Statement

x(dy/dx) = 2xe^x - y + 6x^2

Homework Equations

The Attempt at a Solution

I am trying to show this is an exact differential (book has an answer, it must be )

I rearranged the problem to be :

2xe^x - y + 6x^2 dx = x dy

Partial derivatives (using & for that symbol that represents partial)
&m/&y = -1
&m/&x = 1

-1 doesn't equal 1

Any idea where my mistake is?

 

[Mark44]

Homework Statement

x(dy/dx) = 2xe^x - y + 6x^2

Homework Equations

The Attempt at a Solution

I am trying to show this is an exact differential (book has an answer, it must be )

I rearranged the problem to be :

2xe^x - y + 6x^2 dx = x dy

Partial derivatives (using & for that symbol that represents partial)
&m/&y = -1
&m/&x = 1

-1 doesn't equal 1

Any idea where my mistake is?

Write the equation as Mdx + Ndy = 0, and you'll see that this equation is exact, since M_y = N_x.

 

[illidari]

*face palm*

Thank you lol :P

That would flip the sign of y and make it 1=1.