I was recently given a ODE to solve from a boss at work, with the knowledge that I haven't done them before and this will help me learn. I've spent 10 hours so far learning the basics of ODEs.
The structure of the problem he wrote is essentially:
$$\frac{dB^D(t,T)}{dt} = P_1^D(t) + (K^Q)' \cdot B^D(t,T)$$
*The exponentiated terms are only the letters.
More generally, it is a system of affine ordinary differential equations.
Each matrix has five rows. The $B^D$ matrix has $1$ column and $5$ rows. $(K^Q)'$ matrix has $5$ columns and $5$ rows. $P_1^D(t)$ matrix has $1$ column and $5$ rows.
I'm most familiar with matrix algebra, and said I might solve it that way. But he responded saying that would be immensely difficult, and I should instead solve it by parts. I would like to better understand what he meant. At the moment I have this vague idea that there are two ways to solve it, and one would be too difficult by hand, but the other easier.