Question

Make up a differential equation that you feel confident possesses only the trivial solution$y=0$ . Explain your reasoning.

Short answer

The only solution of $(y\text{'}{)}^2+y^2=0$ is $y=0$.

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.

Make up any differential equation

Start with$y=0$

Make up any differential equation from it.

But make sure it has to be non linear, and make sure it has no negative parts in it.

Because you want it to add up but results is0. The earliest is:

$(y\text{'}{)}^2+y^2=0$

Whatever comes out of the square is positive, so there is no way that the two terms will cancel out in the real numbers domain for any$y>0$or$y<0$.

Thus the only solution of$(y\text{'}{)}^2+y^2=0$is$y=0$.