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Question

The solution of y27y1+12y=0 is

A
y=C1e3x+C2e4x
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B
y=C1xe3x+C2e4x
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C
y=C1e3x+C2xe4x
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D
None of these
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Solution

The correct option is A y=C1e3x+C2e4x
The given equation can be written as (ddx3)(dydx4y)=0
If dydx4y=u then (I) reduces to dudx3u=0
duu=3dxu=C1e3x. Therefore, we have dydx4y=C1e3x which is a linear equation whose I.F. is
e4x.Soddx(ye4x)=C1exye4x=C1ex+C2y=C3x1+C2e4x

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