Question

Find a fundamental set of solutions {ormula1" title=" y_{1}(x) , y_{2}(x) " alt=" y_{1}(x) , y_{2}(x) " align="absmiddle" class="latex-formula">} of the equation
$\frac{d^{2}y}{dx^{2}} + 16 \frac{dy}{dx} + 73y=0$

Answer 1

$\dfrac{\mathrm d^2y}{\mathrm dx^2}+16\dfrac{\mathrm dy}{\mathrm dx}+73y=0\implies r^2+16r+73=0$
$\implies r=-8\pm3i$
$\implies\begin{cases}y_1=e^{-8x}\cos3x\\y_2=e^{-8x}\sin3x\end{cases}$