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CSS Applied Mathematics QUESTION #1301
Question 1
The characteristic equation of \(3y''-6y'+6y=0\) has roots:
  • \(r=1\pm i\)✔️
  • \(r=1\pm 2i\)
  • \(r=-1\pm i\)
  • \(r=2\pm i\)
Correct Answer Explanation
Dividing by 3: \(y''-2y'+2y=0\). Characteristic equation: \(r^2-2r+2=0\Rightarrow r=\dfrac{2\pm\sqrt{4-8}}{2}=\dfrac{2\pm 2i}{2}=1\pm i\). Complementary solution: \(y_c=e^x(C_1\cos x+C_2\sin x)\).