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Q.

If y=c1e2x+c2ex+c3ex satisfies the differential equation d3ydx3+ad2ydx2+bdydx+cy=0 then a3+b3+c3abc is equal to

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a

14

b

12

c

0

d

12

answer is A.

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Detailed Solution

y=C1e2x+C2ex+C3ex
(D2)(D1)(D+1) = 0 D3-(2+1-1)D2+(2-1-2)D2+2=0 d3ydx3-2d2ydx2-dydx+2y=0

a = –2, b = -1, c = 2

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