Question

求微分方程XY''+Y'=0的通解 要详解

Answer 1

解：令p=y'，则有：xp‘+p=0。即x dp/dx+p=0,xdp+pdx=0.得dpx=0,即px=c,即y'x=c.即y'=c/x
得y=lncx+c1,得y=lnx+C(C=lnc+c1)

Answer 2

xy''+y'=0
y'=p
xp'+p=0
p'=-p/x
dp/p=-dx/x
lnp=ln(1/x)+C
p=C'/x
dy/dx=C'/x
y=C'lnx+C0