Given, (2xy dx + dy) e^(x^2) = 0, with the initial condition y(0) = 2. If exact, solve it or if not, then by using the integrating factors solve it and find the particular solution.

Answer 1

2xydx + dy = 0; dy/y = -2xdx; lnIyI = - x² + C; IyI = Ce^{-x^2}; 2 = C; IyI = 2e^{-x^2}