the complete solution of (d*d - 1)y=0 is
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the complete solution of (d*d - 1)y=0 is 1xy
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"Given differential equation is :
(D⁴-1)y=0
Auxiliary equation of above differential equation is
(D⁴-1)=0
=> D⁴=1
=> D²=1,—1
=> D= √1, √—1
=> D=±1, ± i
Hence the general solution is
y = c₁eˣ + c₂e⁻ˣ + e⁰(c₃ cos x + c₄ sin x)
=> y = c₁eˣ + c₂e⁻ˣ + c₃ cos x + c₄ sin x
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