求微分方程dy⼀dx+y⼀x=sinx⼀x的通解

2024-11-14 16:10:16
推荐回答(2个)
回答1:

dy/dx+y/x=sinx/x
==> xdy + ydx = sinx dx
==>咐晌前缓 xdy + ydx - sin x dx = 0
==>衡悔锋 d(xy - cos x) = 0
==> xy - cosx = C

y = (cosx + C)/x

回答2:

xdy+ydx=sinx
xy= -cosx+C
xy+cosx=C