Find the general solution to the differential equation:

$y^{(4)}-y^{(3)}-3y^{\text{'}\text{'}}+5y^{\text{'}}-2y=0$

$($a$)y(x)=C_1{e}^x+C_2{e}^{2x}+C_3{e}^{-x}+C_4{e}^{-2x}$

$($b$)y(x)=C_1{e}^x+C_{2}x{e}^x+C_3{e}^{(1+\sqrt[\phantom{2}]{3})x}+C_4{e}^{(1-\sqrt[\phantom{2}]{3})x}$

$($c$)y(x)=C_1{e}^x+C_{2}x{e}^x+C_3{e}^{-2x}+C_4{x}^2{e}^x$

$($d$)y(x)=C_1{e}^x+C_2{x}^2{e}^x+C_3{e}^{(1+\sqrt[\phantom{2}]{3})x}+C_4{e}^{(1-\sqrt[\phantom{2}]{3})x}$

$($e$)y(x)=C_1{e}^{2x}+C_{2}x{e}^{-x}+C_3{e}^{(1+\sqrt[\phantom{2}]{3})x}+C_4{e}^{(1-\sqrt[\phantom{2}]{3})x}$