Question

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

Answer 1

A first-order differential equation that has the solution y(t) = 3t - 2 can be represented by dy/dt = 3. To verify this solution, we integrate both sides of the equation and determine the constant by using the initial condition. Substituting the value of the constant back into the equation confirms that y(t) = 3t - 2 is a solution.

Step-by-step explanation:

A first-order differential equation that has the solution y(t) = 3t - 2 can be represented as:

dy/dt = 3

Let's verify this solution:

Integrating both sides of the equation, we get:

∫dy = ∫3dt

y = 3t + C

To find the constant C, we use the initial condition y(0) = 0:

0 = 3(0) + C

C = 0

Substituting the value of C back into the equation, we have:

y = 3t

This confirms that y(t) = 3t - 2 is a solution to the given first-order differential equation.