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Question
Solve the following differential equation:
`("d"^2y)/("d"x^2) - 2"k" ("d"y)/("d"x) + "k"^2y = 0`
Solution
Given (D2 – 2kD + k2)y = 0
D = `"d"/("d"x)`
The auxiliary equations is m2 – 2km + k = 0
⇒ (m – k)2 = 0
⇒ m = k, k
Roots are real and equal
The complementary function (C.F) is (Ax + B)ekx
The general solution is y = (Ax + B)ekx
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