求解微分方程dy/dx+x/2y=1/2

原式化为 dy/dx = 1/2 - x/2y令 u = y/x ,y = ux 则：dy/dx = xdu/dx + u代回有 xdu/dx + u = 1/2 - 1/(2u)du/dx = (1/2 - u - 1/(2u))/xdu/( 1/2 - u - 1/(2u)) = dx/x两边积分,再代入 u = y/x 即可