Question

Make up a differential equation that does not possess any real solutions.

Short answer

The differential equation that has no real solution is the ${\left(\frac{dy}{dx}\right)}^2=-1$.

Step-by-step solution

Step 1:Definition of differential equation.

A differential equation is defined as the derivative function of one or more unknown functions (dependable variables) with respect to one or more undependable variables.

Differential equation that has no real solution.

In this problem we have give differential equation that does not posses any real solutions.

For example, ODE

${\left(\frac{dy}{dx}\right)}^2=-1$

On the interval$(-1,1)$has no real solutions.

In fact, it’s solutions is the family$y=\pm ix+c$.

Hence, The differential equation that has no real solution is the ${\left(\frac{dy}{dx}\right)}^2=-1$.