Chapter 1, Problem 1RE

Short answer exercises: Exercises 1-10 focus on the basic ideas, definitions, and vocabulary of this chapter. Their answers arc short (a single sentence or drawing), andyou should be able to do them with little or no computation. However, they vary indifficulty, so think carefully before you answer.
1. Give an example of a first-order differential equation that has the function $y\left(t\right)=2t+3$ as a solution.

To determine

To find the first order differential equation whose solution is $y\left(t\right)=2t+3$ .

Answer to Problem 1RE

  $\frac{dy}{dt}-2=0$

Explanation of Solution

Given:

The function $y\left(t\right)=2t+3$ as a solution of a differential equation.

Calculation:

Differentiating given function with respect to t, we get

  $\begin{array}{l}\frac{dy}{dt}=2\left(1\right)+0\\ \Rightarrow \frac{dy}{dt}=2\\ \Rightarrow \frac{dy}{dt}-2=0\end{array}$

Hence, the first order differential equation with solution $y\left(t\right)=2t+3$ is $\frac{dy}{dt}-2=0$ .