# Are exact differential equations linear differential equation or non-linear?

I'm having a bit of trouble understanding the types of differential equation. I've figured out that for separable differential equations, these equations can either be linear differential equation or non- linear; however, does this apply to exact differential equation as well? (i.e Some exact differential equations are linear, whereas some are non-linear differential equation?) PS. So far I haven't seen any linear exact differential equations

• They can be linear (note that for instance all separable equations are exact, and homogeneous linear equations are separable) but then the usual "exact method" of computing a potential function is not necessary. – Ian Jun 21 at 1:24

The ode $$\frac{dy}{dx}+\frac{y}{x}=0$$ is linear.
Writing it as $$ydx+xdy=0$$. Comparing to standard form $$Mdx+Ndy=0$$, then $$M=y,N=x$$. Checking if exact
\begin{align*} \frac{dM}{dy} & =1\\ \frac{dN}{dx} & =1 \end{align*}
Since $$\frac{dM}{dy}=\frac{dN}{dx}$$ then the linear ODE above is exact. Note also, that if an ODE is not exact, it can still be made exact if one can find an integrating factor.