Given \(\frac{dz}{dx}\) and \(\frac{dz}{dy}\), they are ______ with respect to x and y respectively.
partial derivatives

If \(U=U(x,y,z,t)\), then corresponding total differential equation will be _____

\(Pdx+Qdy+Rdz+Tdt=0\)

In an ordinary or partial differential equation, ____ and its derivatives occur in the degree only and not as higher power or product.
the independent variables

A differential equation involving only ordinary derivatives is called ______
ordinary differential equation

The _____ of a function of two variables \((z=f(x,y))\) with respect to one of the independent is defined as \(\frac{\partial z}{\partial x}=\frac{\partial f}{\partial x}=f_x (x,y)=lim_{\Delta y\rightarrow 0}\frac{f(x+\Delta x,y)-f(x,y)}{\Delta x}\)
partial derivatives

The _____ of a differential equation is order of the highest order derivative appearing in the equation.

Order

A ____ contains two or more dependent variables together with their derivatives with respect to a single independent variable which may or may not exist explicitly into the equation.
total differential equation

The total differential \(du\) of a function \(U(x,y)\) is defined as _____
\(du=\frac{\partial u}{\partial x}dx+\frac{\partial u}{\partial y}dy\)

The ____of a differential equation is the highest exponent of the highest order derivative appearing in it after equation has been expressed in the form free radicals and any fractional power of derivatives.
degree

An equation involving one (or more) dependent variable derivatives with respect to one or one independent variables is called a ______
differential equation

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