Question

I need solutions for this :y"-4y'+3y=exp(x)+exp(-x)

Answer 1

Homogeneous part: characteristic equation
\[\lambda^2-4\lambda+3=0\\(\lambda -3)(\lambda -1)=0\\\lambda = 3\hspace{10pt}or \hspace{10pt}\lambda=1\]

Answer 2

non-homogeneous part: \[\huge y_P= Ce^{-x} + Dxe^x\]
\[\huge Y= y_G +y_P = Ae^{3x}+Be^x+Ce^{-x} + Dxe^x\]

Answer 3

Thank you :)