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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- Jun 13th 2008, 02:40 PMwren17Differential question
Why can both y = x - 3 and y = x + 2 both be considered solutions to the differential equation dy/dx - 1 = 0?

- Jun 13th 2008, 02:46 PMwingless
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.