the c.f for (D^2+1)y=0
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If (D^2+1) y=0, what is the complementary function?
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Chetna Kesarwani
Answered October 13, 2020
Given differential equation is
(D² + 1)y = 0 ; D≡d/dx
Corresponding auxiliary equation is
D² + 1 = 0
=> D² = —1
=> D = √—1
=> D = ±i
∴ C.F. = e⁰ˣ[c₁ cos x + c₂ sin x]
=> C.F. = 1[c₁ cos x + c₂ sin x]
=> C.F. = c₁ cos x + c₂ sin x
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