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The solution of the differential equation dy/dx = ky, y(0) = c is

1. x = ce^(-kx)
2. x = ke^x
3. y = ce^(kx)
4. y = ce^(-kx)

Correct answer: y = ce^(kx)

Solution

The solution to the differential equation dy/dx = ky is derived from the separation of variables and integration, leading to an exponential function where the constant c represents the initial condition y(0) = c, resulting in y = ce^(kx).

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