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Find the general solution of the differential equation d²y/dx² - 2 dy/dx + y = 0.
- y = (c1 + c2 x) e^x
- y = c1 e^x + c2 e^x
- y = (c1 x) e^x
- none of these
Correct answer: y = (c1 + c2 x) e^x
Solution
The characteristic equation m² - 2m + 1 = 0 has a repeated root m = 1, so the general solution is y = (c1 + c2 x) e^x.
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