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In this problem, y = c1ex c2e-x is a two-parameter family of solutions of the second-order differential equation y" - y = 0. Find c1 and c2 given the following initial conditions.

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Final answer:

The question is about determining the values of the constants c1 and c2 in the solution of a second-order differential equation using the given initial conditions. The process involves finding the first derivative of the solution and creating a system of equations with the initial conditions.

Step-by-step explanation:

The student's question involves solving a second-order differential equation with initial conditions. Given y = c1ex + c2e-x as the solution to the differential equation y" - y = 0, the constants c1 and c2 can be determined using the provided initial conditions. To find these constants, we first compute the first derivative, y' = c1ex - c2e-x, and then apply the initial conditions to solve for c1 and c2. The initial conditions have not been provided in the student's question, but the process would involve setting up a system of equations using the initial values for y and y' at a particular x value (usually x=0 if not specified otherwise), and then solving this system for the constants.

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