Question

微分方程x(dy/dx)=y+x^2 sin x的通解是

Answer 1

x(dy/dx)=y+x^2 sin x => x * y ' - y = x^2 * sin x => 两边除以 x^2

( x * y ' - y) / x^2 = (y/x) ' = sin x => 两边积分

y/x = - cos x + C =>

y = x * (C - cos x),C为任意常数.