EDB — 1T6

Exercises

1. [1T6]Prerequisites:[1MN]↺↻,[1MK]↺↻,[1T1]↺↻.

   Let be given \(C∈ ℂ^{n× n}\), \(F,A:ℝ→ℂ^{n× n}\) continuous, and the solution \(Y(t)\) of the ODE

   \[ \frac{d\hskip5.5pt}{d{t}} Y(t) = A(t) Y(t)~ ~ ~ ,~ ~ ~ Y(0)=\mathrm{Id}~ ~ . \]

   Solve the equation

   \[ X'=AX+F~ ~ , X(0)=C~ ~ , \]

   where \(X:ℝ→ℂ^{n× n}\), using \(Y(t)\) as an auxiliary function.

   Solution 1

   [1T7]↺↻