The discussion focuses on solving a nonhomogeneous second-order differential equation represented by xy'' - 2y' = -2/x² with initial conditions y(1) = -1/3 and y'(1) = 1. The user seeks assistance specifically using the method of constant variation, which they are familiar with, but also expresses openness to alternative methods. A suggested approach involves transforming the equation into a first-order ordinary differential equation (ODE) for u = y', leading to the equation u' - 2/x * u = -2/x³, which can be solved using an integrating factor.
PREREQUISITESStudents and professionals in mathematics, particularly those studying differential equations, as well as educators looking for effective teaching methods for solving nonhomogeneous second-order differential equations.
darjiaus7 said:Hello guys . I want to do nonhomogeneous 2nd order dif equation..I am trying to do this for 2 days , but I can't get good answer. Can you show me how to do this equation with constant variation method ( i know it best) or other I would be very gratefull , because after 2 days of trying I am surrendered... xy''-2y' = -\frac{2}{x^2} ; y(1)=-\frac{1}{3} ; y'(1)=1