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Step-by-step explanation:
A complete solution contains the same number of arbitrary constants as the order of the original equation. (This is because, in order to solve a differential equation of the nnth order, you will integrate nn times, each time adding a new arbitrary constant.) Since our example above is a first-order equation, it will have just one arbitrary constant in the complete solution. Therefore, the general solution is f(x)=Ce−xf(x)=Ce−x, where CC stands for an arbitrary constant. You can see that the differential equation still holds true with this constant. For a specific solution, replace the constants in the general solution with actual numeric values.
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