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CSS Applied Mathematics QUESTION #1325
Question 1
For the ODE \(y''-2y'+2y=0\), the general solution using roots \(r=1\pm i\) is:
  • \(y=e^x(C_1+C_2 x)\)
  • \(y=C_1e^x\cos x+C_2e^x\sin x\)✔️
  • \(y=C_1\cos x+C_2\sin x\)
  • \(y=e^{-x}(C_1\cos x+C_2\sin x)\)
Correct Answer Explanation
For complex roots \(r=\alpha\pm\beta i\), the real general solution is \(y=e^{\alpha x}(C_1\cos\beta x+C_2\sin\beta x)\). Here \(\alpha=1\), \(\beta=1\), so \(y=e^x(C_1\cos x+C_2\sin x)\).