Question

the c.f for (D^2+1)y=0​

Answer 1

Answer:

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