For the second-order LDE y'' − 5y' + 6y = 0, the auxiliary equation m²…

Question

For the second-order LDE y'' − 5y' + 6y = 0, the auxiliary equation m² − 5m + 6 = 0 has roots m = 2, 3. The general solution is:

Accepted Answer

C. $y = A e^{2x} + B e^{3x}$ (sum of exponentials)

2 distinct real roots m1, m2 → general solution: y = Ae^(m1 x) + Be^(m2 x). For m = 2, 3: y = Ae^(2x) + Be^(3x). The (A + Bx) form is for equal roots only.

Answer

$y = A e^{2x} \cdot B e^{3x}$ (product)

Answer

$y = e^{2x + 3x}$ (sum exponent)

Answer

$y = (A + Bx) e^{2.5x}$ (linear in x)