Question

Give an example of a first-order differential equation that the solution y(t)=2t+3 a solution

Answer 1

To find a first-order differential equation for y(t) = 2t + 3, we differentiate y(t) to get dy/dt = 2, giving us a simple linear differential equation with a constant rate of change.

Step-by-step explanation:

To find a first-order differential equation for which y(t) = 2t + 3 is a solution, we start by differentiating y(t) with respect to t, which will give us the derivative dy/dt. Calculus tells us that the derivative of y(t) = 2t + 3 with respect to t is 2, as the derivative of a constant, like 3, is zero and the derivative of 2t with respect to t is 2. Therefore, a simple first-order differential equation that satisfies this condition is:

dy/dt = 2

This is an example of a linear differential equation with a constant rate of change.