Question

6 points 9. Find an appropriate integrating factor. DO NOT SOLVE

Answer 1

(2y^2 + 3x) dx + xy dy = 0 rightwardsdoublearrow 2y^2 + 3x + xy dy/dx = 0 rightwardsdoublearrow dy/dx + 2y^2 + 3x/xy = 0 rightwardsdoublearrow dy/dx + (2/x) y = -3/y rightwardsdoublearrow y dy/dx + (2/x) y^2 = -3 Letting u = y^2: du/dx = 2y dy/dx rightwardsdoublearrow 1/2 du/dx + (2/x) u = -3 rightwardsdoublearrow du/dx + (4/x) u = -6 for an ODE in the form dp/dt + f(t) P = g(t), the integrating factor, mu is Given by: integral f(t) dt mu = e rightwardsdoublearrow mu = e^integral 4/x dx = e^4 ln (x) = x^4