Question

dy/dx+y/x=1的通解？

帮忙解一下哈

Answer 1

两边乘以 xdx，化为
xdy+ydx=xdx，
即 d(xy) = d(1/2 * x^2)，
积分得 xy=1/2 * x^2+C 。

Answer 2

p(x) = 1/x
∫p(x)dx =ln|x| +C
e^[∫p(x)dx] = x
dy/dx+y/x=1
两边乘以x
x(dy/dx+y/x)=x
d/dx (xy) =x
xy =∫ x dx
=(1/2)x^2 +C
y=(1/2)x +C/x