grandes-ecoles 2024 Q22

grandes-ecoles · France · polytechnique-maths-b__mp Second order differential equations Reduction of a differential system to a second-order ODE
Solve the differential system $$\left\{ \begin{array}{l} x'(t) = x(t) - \cos(t) y(t) \\ y'(t) = \cos(t) x(t) + y(t) \end{array} \right.$$ and determine its normal form (see question 16d).
Solve the differential system
$$\left\{ \begin{array}{l} x'(t) = x(t) - \cos(t) y(t) \\ y'(t) = \cos(t) x(t) + y(t) \end{array} \right.$$
and determine its normal form (see question 16d).