grandes-ecoles 2014 QIID1

grandes-ecoles · France · centrale-maths1__pc Second order differential equations Reduction of a differential system to a second-order ODE

We denote by $A$ a real square matrix of size 2 and we set, for all $x$ in $\mathbb{R}^2$, $f(x) = Ax$. For $a$ in $\mathbb{R}^2$, we denote by $u_a(t)$ the solution on $\mathbb{R}$ of the Cauchy problem $$X' = AX, \quad X(0) = a$$
Revisit questions II.B.1 and II.B.2 in the case where $A$ is triangular of the form $$A = \begin{pmatrix} \lambda & \mu \\ 0 & \lambda \end{pmatrix}$$

We denote by $A$ a real square matrix of size 2 and we set, for all $x$ in $\mathbb{R}^2$, $f(x) = Ax$. For $a$ in $\mathbb{R}^2$, we denote by $u_a(t)$ the solution on $\mathbb{R}$ of the Cauchy problem
$$X' = AX, \quad X(0) = a$$

Revisit questions II.B.1 and II.B.2 in the case where $A$ is triangular of the form
$$A = \begin{pmatrix} \lambda & \mu \\ 0 & \lambda \end{pmatrix}$$

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