What is the general solution of the second-order homogeneous differential equation d^2y/dx^2 - 6 dy/dx + 9y = 0?
Answer and explanation
Correct answer: B. (C1 + C2 x) e^(3x)
- Step 1: Write the characteristic equation: m^2 - 6m + 9 = 0.
- Step 2: Factoring gives: (m - 3)^2 = 0, which has repeated roots m = 3, 3.
- Step 3: For repeated roots, the complementary function is y = (C1 + C2 x) e^(m x).
- Step 4: Thus, y = (C1 + C2 x) e^(3x).
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