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.
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.