Why can both y = x - 3 and y = x + 2 both be considered solutions to the differential equation dy/dx - 1 = 0?
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Because, $\displaystyle \frac{dy}{dx}=1$ $\displaystyle dy = dx$ $\displaystyle y = x + C$ So any solution in the form $\displaystyle y=x+C$ is correct.
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