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CSS Applied Mathematics QUESTION #4150
Question 1
What is the general solution of $y'' - 3y' + 2y = 0$?
  • $y = c_1e^x + c_2e^{2x}$✔️
  • $y = c_1e^{-x} + c_2e^{-2x}$
  • $y = c_1\cos(x) + c_2\sin(x)$
  • $y = e^x(c_1 + c_2x)$
Correct Answer Explanation
Characteristic: $r^2 - 3r + 2 = 0 \Rightarrow (r-1)(r-2) = 0 \Rightarrow r = 1, 2$. General solution: $y = c_1e^x + c_2e^{2x}$.