Question

the Eistence and Uni -xy+ 2x)

diff eq

Answer 1

step by step resolution of the equation (3x^2 y^3 -y^2 + y) d x + (-z.y + 2.x) d y = 0 finding an root of the polynomial p(x) = (3.x^2 y^3-y^2 + y) d.x + (-x.y + 2.x)d.y 1. p(0) = 0, 0 is a root of the polynomial 2. the polynomial can be written in the form p(x) = (x).(a.x^2 + b.x + c) 1. we can determine a, b, c by replacing by 1, 2 and 3 solving of the systems of 3 equations with 3 unknowns 2. the system to be solved is [a + b + c = (3.y^3-y^2 + y).d(-y + 2).d.y;2.(a.4 + b.2 + c) = (12.y^3-y^2 + y) d.2 + (-2.y + 4)d.y;3.(a.9 + b.3 + c) = (27.y^3-y^2 + y).d.3 the solution of the system is [a = --36 y^3 d/12: b = 0;c = --36 y d + 24 y^2 d/12] the polynomial is written as p(x) = (z).(--36 y.d + 24 y^2 d/12 + 3 y^3 d x^2) 3. solving the following quadratic equation = -36y.d + 24 y^2 d/12 + 3 y^3 d x^2 step by step resolution of the equations = -36.y.d + 24.y^2d/12 + 3 y^3 d x^2 = 0