The discussion focuses on solving the exact differential equation x(dy/dx) = 2xe^x - y + 6x^2. The user initially attempts to demonstrate that the equation is exact by calculating partial derivatives, resulting in a contradiction. However, the correct approach involves rewriting the equation in the form Mdx + Ndy = 0, which confirms its exactness since the condition My = Nx holds true. The solution highlights the importance of proper rearrangement in identifying exact differentials.
PREREQUISITESStudents studying calculus, particularly those focused on differential equations, as well as educators looking for examples of exact differentials and their solutions.
Write the equation as Mdx + Ndy = 0, and you'll see that this equation is exact, since My = Nx.illidari said: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?