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The differential equation of the family ...

The differential equation of the family `y = ae^(x) + bx e^(x) + vx^(2) e^(x)` curves, where a, b, c are arbitrary constants, is :

A

`y'''+ 3y'' + 3y'+ y = 0`

B

`y'''+ 3y'' - 3y'- y = 0`

C

`y'''- 3y'' -3y'+ y = 0`

D

`y'''- 3y'' + 3y'- y = 0`

Text Solution

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The correct Answer is:
D
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