Question

Answer Problems1-12without referring back to the text. Fill in the blanks or answer true or false.

By inspection, two solutions of the differential equation${\mathit{y}}^{\cancel{\mathbf{c}}}\mathbf{+}\left|y\right|\mathbf{=}\mathbf{2}$ are

Short answer

The two solutions are $y=\pm 2$.

Step-by-step solution

Definition

A differential equation is an equation with one or more derivatives of a function.

Solve given equation

Let $\frac{dy}{dx}=0$, then

$\begin{array}{rcl}\left|y\right|-2& =& 0\\ \left|y\right|& =& 2\\ y& =& \pm 2\end{array}$

So, when plugging the solutions$\begin{array}{rcl}y& =& \pm 2\end{array}$into the differential equation, we only need to check about the term $\left|y\right|$.