Question:medium
The differential equation of the family \( y = a e^{x} + b x e^{x} + c x^{2} e^{x} \) is
The differential equation of the family \( y = a e^{x} + b x e^{x} + c x^{2} e^{x} \) is
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A repeated root 'r' of multiplicity 'k' in a linear ODE leads to solutions $e^{rx}, xe^{rx}, ..., x^{k-1}e^{rx}$.
Updated On: Apr 10, 2026
- $y''' + 3y'' + 3y' + y = 0$
- $y''' + 3y'' - 3y' - y = 0$
- $y''' - 3y'' - 3y' + y = 0$
- $y''' - 3y'' + 3y' - y = 0$
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The Correct Option is D
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