Solve the linear homogeneous equation \[ D^2y - 5Dy + 6y = 0 \]
Answer : **Solution:** 1. **Write the auxiliary equation:** \[ m^2 - 5m + 6 = 0 \] 2. **Factorizing the equation:** \[ (m - 2)(m - 3) = 0 \] So, \( m = 2, 3 \). 3. **General ... ** Since both roots are real and distinct, the solution is: \[ y = C_1 e^{2x} + C_2 e^{3x} \]...
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