Question

函数y=f(x)满足微分方程xdy+ydx=0,且f(3)=4,则f(2)等于多少？

Answer 1

xdy=-ydx
dy/y = -dx/x
两边积分得到
lny =-lnx +C
f(3)=4带入得到
ln4=-ln3 +C, C=ln(12)
y=e^(-lnx +ln(12)) = e^ln(12/x)=12/x
f(2)=12/2 =6

Answer 2

xdy+ydx=0
xdy=-ydx
∫ dy/y = -∫dx/x
ln|y| = -ln|x| + C'
y= C/x
y(3)=4
4=C/3
C=12
ie
y=12/x
y(2)= 12/2 =6