Question

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

Answer 1

Given the differential equation: $y'''+3y''+3y'+y=0$

Require to find the general solution of the given differential equation.

An Auxiliary Equation corresponding to the given homogeneous linear differential equation is

$m^3+3m^2+3m+1=0$

$\Rightarrow (m+1)^3=0$

$\Rightarrow m=-1,-1,-1$

The general solution to the given differential equation is

$y(x)=(c_1+c_2x+c_3x^2)e^{-x}$

Therefore, general solution to the given differential equation is

$y(x)=(c_1+c_2x+c_3x^2)e^{-x}$