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The differential equation of the family $y=ae^x+bx\; e^x+cx^2\;e^x$ of curves, where $a,b,c$ are arbitrary constants, is :

\[\begin {array} {1 1} (1)\;y'''+3y''+3y'+y=0 & \quad (2)\;y'''+3y''-3y'-y=0 \\ (3)\;y'''+3y''-3y'+y=0 & \quad (4)\;y'''-3y''+3y'-y=0 \end {array}\]

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$ (4)\;y'''-3y''+3y'-y=0 $
answered Nov 7, 2013 by pady_1

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