Question

Answer Problems 1-12without referring back to the text. Fill in the blanks or answer true or false.

The linear DE, ${\mathit{y}}^{\cancel{\mathbf{c}}}\mathbf{+}{\mathit{k}}_{\mathbf{1}}\mathit{y}\mathbf{=}{\mathit{k}}_{\mathbf{2}}$, where k₁and k₂are nonzero constants, always possesses a constant solution.

Short answer

True.

Step-by-step solution

Definition

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

Substitute values

Let equation be$y=\frac{k_2}{k_1}$

Then y' = 0 as both k₁,k₂, are constants.

Substituting values in differential equation y' + k₁y = k₂ we get

$\begin{array}{rcl}\left(0\right)+k_1\left(\frac{k_2}{k_1}\right)& =& 0+k_2\\ & =& k_2\end{array}$

So this differential equation have constant solution.

Hence given statement is true.