grandes-ecoles 2010 QII.C

grandes-ecoles · France · centrale-maths1__psi Differential equations Higher-Order and Special DEs (Proof/Theory)

We study the differential equation $$y(x) y'(x) = -4x \tag{E}$$
II.C.1) Recall the statement of the existence and uniqueness theorem for maximal solutions of a nonlinear scalar differential equation subject to Cauchy conditions. II.C.2) Explain how, and possibly to what extent, this theorem applies to $(E)$. II.C.3) Are the maximal solutions given by this theorem maximal solutions of $(E)$? II.C.4) Deduce from the previous questions the maximal solutions of $(E)$.

We study the differential equation
$$y(x) y'(x) = -4x \tag{E}$$

II.C.1) Recall the statement of the existence and uniqueness theorem for maximal solutions of a nonlinear scalar differential equation subject to Cauchy conditions.\\
II.C.2) Explain how, and possibly to what extent, this theorem applies to $(E)$.\\
II.C.3) Are the maximal solutions given by this theorem maximal solutions of $(E)$?\\
II.C.4) Deduce from the previous questions the maximal solutions of $(E)$.

Paper Questions

QI.A QI.B QI.C QI.D QI.E QII.A QII.B QII.C QII.D QIII.A QIII.B QIII.C QIII.D