- Thread starter idontknow
- Start date

from a very old book , it is an exact DE.Just out of curiousity, where are you getting these DEqs from?

-Dan

In this section we will discuss identifying and solving exact differential equations. We will develop of a test that can be used to identify exact differential equations and give a detailed explanation of the solution process. We will also do a few more interval of validity problems here as well.

tutorial.math.lamar.edu

\(\displaystyle 1 + \left ( e^y - x \right ) \dfrac{dy}{dx} = 0\)

and you have the general form

\(\displaystyle M(x, y) + N(x, y) \dfrac{dy}{dx} = 0\)

then what are M(x, y) and N(x, y) and how do you use them?

Let us know what you've got and we'll go from there. The solution method isn't particularly hard but it does require some intuition.

-Dan

Integrating with respect to y gives $e^{-y}x = -y + \text{C}$, where $\text{C}$ is a constant,

so $x = (\text{C} - y)e^y$.

Nice!

Integrating with respect to y gives $e^{-y}x = -y + \text{C}$, where $\text{C}$ is a constant,

so $x = (\text{C} - y)e^y$.

-Dan