grandes-ecoles 2019 Q1

grandes-ecoles · France · centrale-maths1__psi Differential equations First-Order Linear DE: General Solution

Let $\alpha$ be a real number. We denote $f_{\alpha} : x \longmapsto (1-x)^{-\alpha}$.
Specify the domain of definition $D$ of $f_{\alpha}$. Justify that $f_{\alpha}$ is of class $C^{1}$ on $D$ and give a first-order linear differential equation satisfied by $f_{\alpha}$ on $D$.

Let $\alpha$ be a real number. We denote $f_{\alpha} : x \longmapsto (1-x)^{-\alpha}$.

Specify the domain of definition $D$ of $f_{\alpha}$. Justify that $f_{\alpha}$ is of class $C^{1}$ on $D$ and give a first-order linear differential equation satisfied by $f_{\alpha}$ on $D$.

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