Understanding and solving exact differential equations can be tough for Year 13 students. These equations usually look like this:

$M(x, y)dx + N(x, y)dy = 0$

Here, $M$ and $N$ are functions that depend on $x$ and $y$.

To check if an equation is exact, you need to see if

$\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$

This can be tricky since finding partial derivatives is not always easy, especially with complex functions.

If the equation is exact, you can find a solution by integrating $M$ with respect to $x$ and $N$ with respect to $y$. But this can get complicated if the functions are hard to integrate.

Also, if the equation isn’t exact, you might need to find an integrating factor to make it exact. This process can feel like guesswork and sometimes becomes frustrating.

However, if you stick with it and practice, you can become successful at solving these equations!