The order of a differential equation, which is either an ordinary differential equation or a partial differential equation. The order of a differential equation is the order of the highest derivative appearing in the equation. For example, okay, differential equation three, which is an ordinary differential equation, e to the x times y''- 3 times y' square + 2xy = x times e to the x. This is a second order ordinary deferential equation, because the highest derivative involved for the unknown y is 2, right? On the other hand, the partial differential equation, the so-called wave equation, equation number two right here, this is second order partial differential equation, right? Because the highest order derivative involved is second derivative of u, and either the t variable or the x variable, okay? Or if you think about the ordinary differential equation, equation one, okay? This is a second order ordinary differential equation in h, or this is a first order differential equation in v, okay? Then the most general nth order differential equation may be written as capital F of x, y, y', and nth derivative of y, is equal to 0. Where the capital F is a real-valued function of n + 2 variables, say, x, y, y', and nth derivative of y, okay? If we can solve this equation, equation number four, for its highest order derivative, say nth derivative of y as, okay? nth derivative of y is equal to f(x, y, y' (n- 1) derivative of y), okay? Then we call this equation number five as the normal form of the equation number four, okay? Here, I'll remind you what is the equation number four, okay? Equation number four Is capital F(x, y, y', and nth derivative of y), and that is equal to 0, right? What I mean here is, if you can solve this equation for its highest order derivative, nth derivative of y, in this form, okay. nth derivative of y is equal to function of all the other variables. Then we call this equation to be the normal form of this equation. For example, let's consider the equation number three again, which was, Here the equation number three, let me copy it down here. Equation number three is e to the x y''- 3 y' squared + 2xy = x times e to the x right, that's the equation number three, right. And we know that this is a second order ordinary differential equation, okay? What is the normal form of this equation? Normal form of any such ordinary differential equation is, we needed to express it as the highest possible derivative of y, that is y'' in this case, as a function of all the other variables, okay? So you can simply try to first divide this equation value to the x. Then you'll get y''- 3e to the -x y' squared + 2xe to the -x times y = x, right? Then try to solve this equation for the highest order derivative of y, say y'', okay? Then we will get, y'' = 3e to the -x y' squared- 2x times e to the -x times y + x, right? Down here, okay, this is the normal form of the original equation number three. Sometimes, we write a first order ordinary differential equation. Say, y' = dy over dx = -M(x, y) over N(x, y) as M(x, y)dx + N(x, y)dy = 0. This is another common expression of the first order differential equation.