Can you check my answer?

[hank]

Find the general solution of the given higher-order DE.

y^"" - 2y" + y = 0
m^4 - 2m^2 + 1 = 0 //auxiliary equation.
(m^2 - 1)(m^2 + 1) = 0 //Factoring
(m+1)(m-1)(m+1)(m-1) = 0 //Factoring again
m1 = m2 = 1, m3 = m4 = -1
y = C1e^x + C2xe^x + C3e^-x + C4xe^-x

Thanks in advance.

 

[Deleted member 4993]

Find the general solution of the given higher-order DE.

y^"" - 2y" + y = 0
m^4 - 2m^2 + 1 = 0 //auxiliary equation.
(m^2 - 1)(m^2 + 1) = 0 //Factoring
(m+1)(m-1)(m+1)(m-1) = 0 //Factoring again <<<< where did that come from?

m[sup:2rzoaeo7]2[/sup:2rzoaeo7] + 1 = 0

(m + i)(m - i) = 0

Now continue.....

m1 = m2 = 1, m3 = m4 = -1
y = C1e^x + C2xe^x + C3e^-x + C4xe^-x

Thanks in advance.