Answer to Question #284192 in Differential Equations for ASAP

Question

IV. Find the general solution of the given differential equation.

11/234) y‴ − y″ − y′ + y = 0

14/234) y^(4) − 4y‴ + 4y″ = 0

Answer 1

$11/234) y'''-y''-y'+y=0\\ \lambda^3-\lambda^2-\lambda+1=0\\ \lambda^2(\lambda-1)-(\lambda-1)=0\\ (\lambda-1)(\lambda^2-1)=0\\ (\lambda-1)^2(\lambda+1)=0\\ \lambda_1=\lambda_2=1, \lambda_3=-1\\ y=c_1e^x+c_2xe^x+c_3e^{-x}.\\ \\ 14/234) y^{(4)}-4y'''+4y''=0\\ \lambda^4-4\lambda^3+4\lambda^2=0\\ \lambda^2(\lambda^2-4\lambda+4)=0\\ \lambda^2(\lambda-2)^2=0\\ \lambda_1=\lambda_2=0, \lambda_3=\lambda_4=2\\ y=c_1+c_2x+c_3e^{2x}+c_4xe^{2x}$