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प्रश्न
Solve the following differential equation:
`("d"^2y)/("d"x^2) - 6 ("d"y)/("d"x) + 8y = 0`
उत्तर
Given (D2 – 6D + 8)y = 0
D = `"d"/("d"x)`
The auxiliary equations is
m2 – 6m + 8 = 0
(m – 4)(m – 2) = 0
m = 4, 2
Roots are real and different
The complementary function (C.F) is (Ae4x + Be2x)
The general solution is y = Ae4x + Be2x
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