Final answer:
The function y = e^rx satisfies a differential equation depending on the specific values of r. One must substitute y into the differential equation, solve for r by differentiating and equating, which generally confirms y as a solution for the values of r found.
Step-by-step explanation:
The student is asking about the values of r for which the function y = erx satisfies a given differential equation. Without the specific differential equation provided, we cannot give a precise answer. However, in general, when given a differential equation, one can substitute the proposed function y = erx into the differential equation and solve for r. This process usually involves taking the derivative of the function with respect to x, substituting it back into the differential equation, and finding the value of r that makes the equation true for all x.
For example, if we consider a simple differential equation dy/dx = ry, by substituting y = erx into it and differentiating, we get r times the function itself. Solving rerx = r erx confirms that the original function is indeed a solution for any real number value of r. Therefore, the process is highly dependent on the form of the differential equation given.