Question

Which of the following are differential equations ?

• A. $\frac{dz}{dy}=z$
• B. $\frac{dz}{dy}\times z=0$
• C. $x^2+y^2+2xy+2x-3y+25=0$
• D. $w^2+d^2+\frac{dw}{dx}+5=0$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $\frac{dz}{dy}=z$
B $\frac{dz}{dy}\times z=0$
D $w^2+d^2+\frac{dw}{dx}+5=0$

We can easily answer this question if we know what differential equation is. Let’s look at how differential equation is defined even though it is somewhat easy to guess from the name itself. An equation involving independent and dependent variable and the derivatives of the dependent variables is called differential equation.
Basically, we have to look if there is derivative in the given equations. Even an equation of the form $\frac{dy}{dx}=0$ is called a differential equation. Here, the dependent variable is y and independent variable is x.
If we go through the options, we see that the only equation without a derivative is $x^2+y^2+2xy+2x-3y+25=0$. Everything else is a differential equation.