Question

Determine the differential equation arising from y=c₁e^5x+c₂e^7x

Answer 1

$\text{Given the the solution $y=c_1e^{5x}+c_2e^{7x}$, we know that}\\\text{$k_1=5$ and $k_2=7$} \\\text{The complimentary solution is}\\(k-5)(k-7)=0\\=k^2-12k+35=0 \\\text{Therefore the differential equation is}\\y''-12y'+35y=0$