Question

The equation $\frac{dy}{dx}+\frac{dz}{dx}\sin x=0$ is a partial differential equation because we are differentiating independent variables $y$ and $z$ partially in this differentiation equation

• A. True
• B. False

Answer 1

The correct option is B False

We want to know if the given differential equation is a partial differentiation equation. For that we need to know what partial differential equations are. We call a differential equation a partial differential equation if the dependent variables depend on more than one independent variable. We have to look if we are differentiating with respect to more than one variable. Given differential equation is $\frac{dy}{dx}+\frac{dz}{dx}\sin x$ = 0. In this equation the dependent variables $y$ and $z$ depend only on $x$ or the derivative is calculated only with respect to $x$. This means the given equation is not a partial differential equation. Let’s look at an example of partial differential equation. If we have terms like $\frac{df}{dz}$ and $\frac{df}{dy}$ we write them as $\frac{\partial f}{\partial z}$ and $\frac{\partial f}{\partial y}$
$\frac{\partial f}{\partial x}+y\frac{\partial f}{\partial y}+x=0$ is an example of partial differential equation. Here the dependent variable $f$ depends on more than one independent variables, $x$ and $y$.