## First-order LSEs with constant coefficients: Repeated roots (continued)

In an earlier blog post, I showed the solution to a first-order linear system of two (ordinary) differential equations with constant coefficients for the case where the characteristic equation of the (constant coefficient) square matrix has repeated roots. In particular, I considered the system $\begin{array}{rcl}\frac{\mathrm{d}x}{\mathrm{d}t}&=&ax+by\\ \frac{\mathrm{d}y}{\mathrm{d}t}&=&cx+dy\\\end{array}$, where $a,b,c,d$ are real constants and $x,y,t$ are real variables, for the case where $(a-d)^2+4bc=0$ and $a\ne d$. Now I look at the case where $a=d$. Continue reading “First-order LSEs with constant coefficients: Repeated roots (continued)”