Solve the given differential equation by undetermined coefficients method.

$y^{\text{'}\text{'}}-8y^{\text{'}}+16y=24x+2$

a$)y=c_1{e}^{4x}+c_2{e}^{4x}+\frac{3}{2}x+\frac{7}{8}$

b$)y=c_1{e}^{4x}+c_{2}x{e}^{4x}+\frac{3}{2}x+\frac{7}{8}$

c$)y=c_1{e}^{4x}+c_{2}x{e}^{4x}+\frac{3}{2}+\frac{7}{8}x$

d$)y=c_1{e}^{4x}+c_2{e}^{4x}+\frac{3}{2}+\frac{8}{7}x$

e$)y=c_{1}x{e}^{4x}+c_{2}x{e}^{4x}+\frac{3}{2}x+\frac{7}{8}x$