Final answer:
The student's question involves finding solutions to a differential equation by taking derivatives and substituting them into the equation to verify correctness.
Step-by-step explanation:
The question pertains to the verification of solutions to a differential equation. The steps to prove that given functions are solutions involve taking their first and second derivatives with respect to an independent variable, often time, and substituting these into the given differential equation. This process is commonly used in mathematics to verify solutions to differential equations, which often arise in the modeling of physical phenomena.
For instance, if the differential equation is given in the form of 'Equation 15.23,' you would substitute the proposed solutions into this equation to see if the equation is satisfied. If so, this confirms that the functions are indeed solutions. This method can be applied to a variety of differential equations, including those that result in logistic curves or require understanding the equilibrium points in systems of equations.