求微分方程dy/dx+y/x=cosx的通解
问题描述：
求微分方程dy/dx+y/x=cosx的通解
答
dy/dx + y/x = cosx
积分因子 = e^∫ 1/x dx = e^ln|x| = x,乘以方程两边
x · dy/dx + y = xcosx
d(xy)/dx = xcosx
xy = ∫ xcosx dx
xy = ∫ x d(sinx) = xsinx - ∫ sinx dx = xsinx + cosx + C
y = sinx + (cosx)/x + C/x