Question

Find the real-valued general solution of the differential equation

y''+8y'+8y=0

Answer 1

\[y''+8y'+8y=0\]
\[y=Ae^{m_1}+Be^{m_2}\]
\[m^2+8m+8=0\]\[m=\frac{-8\pm\sqrt{8^2-4\times 8}}{2} \]\[m=-4\pm\frac{\sqrt{32}}{2} \]\[m=-4\pm2\sqrt2\]

\[y=Ae^{-4+2\sqrt2}+Be^{-4-2\sqrt 2}\]