Answer:
[tex]y(x)=C_1e^{4x}+C_2e^{4x}[/tex]
Step-by-step explanation:
To solve a second-order homogeneous differential equation, we need to substitute each term with the auxiliary equation [tex]am^2+bm+c=0[/tex] where the values of [tex]m[/tex] are the roots:
[tex]y''-8y'+16y=0\\\\m^2-8m+16=0\\\\(m-4)^2=0\\\\m-4=0\\\\m=4[/tex]
Since the values of [tex]m[/tex] are equal real roots, then the general solution is [tex]y(x)=C_1e^{m_1x}+C_2e^{m_1x}[/tex]
Thus, the general solution for our given differential equation is [tex]y(x)=C_1e^{4x}+C_2e^{4x}[/tex]
