The general solution for the DE $y^{\text{'}\text{'}}-5y^{\text{'}}+6y=e^{4x},$ is given by

c$.y=c_1{e}^{2x}+c_2{e}^{-3x}+\frac{1}{4}{e}^{4x}$

d$.y=c_1{e}^{2x}+c_2{e}^{3x}+\frac{1}{2}{e}^{4x}$

b$.y=c_1{e}^{2x}+c_2{e}^{3x}+\frac{1}{8}{e}^{4x}$

e$.$ None of these

a$.y=c_1{e}^{2x}+c_2{e}^{3x}+\frac{1}{4}{e}^{4x}$