Taking the first and second derivatives of \(y\) with respect to \(x\), we have:
\(y' = re^{rx}\)
\(y'' = r^2e^{rx}\)
Substituting these expressions into the differential equation, we get:
\(2r^2e^{rx} - 4re^{rx} + 8e^{rx} = 0\)
Factoring out \(e^{rx}\), we
Show more…