微积分问题:(xy)'=y'y'=(xy)' dy/dx=d(xy)/dx dy/dx=y+xdy/dx (1-x)dy/dx=y 1/ydy=1/(1-x)dx lny=ln|1-x|+C y=c(x-1)可代回去:y'=c (xy)=c(x^2-x) (xy)'=c(2x-1)两个又不相等了,为什么?错了哪里?
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![微积分问题:(xy)'=y'y'=(xy)' dy/dx=d(xy)/dx dy/dx=y+xdy/dx (1-x)dy/dx=y 1/ydy=1/(1-x)dx lny=ln|1-x|+C y=c(x-1)可代回去:y'=c (xy)=c(x^2-x) (xy)'=c(2x-1)两个又不相等了,为什么?错了哪里?](/uploads/image/z/12505615-7-5.jpg?t=%E5%BE%AE%E7%A7%AF%E5%88%86%E9%97%AE%E9%A2%98%3A%28xy%29%27%3Dy%27y%27%3D%28xy%29%27+dy%2Fdx%3Dd%28xy%29%2Fdx+dy%2Fdx%3Dy%2Bxdy%2Fdx+%281-x%29dy%2Fdx%3Dy+1%2Fydy%3D1%2F%281-x%29dx+lny%3Dln%7C1-x%7C%2BC+y%3Dc%28x-1%29%E5%8F%AF%E4%BB%A3%E5%9B%9E%E5%8E%BB%3Ay%27%3Dc+++++++%28xy%29%3Dc%28x%5E2-x%29+++++%28xy%29%27%3Dc%282x-1%29%E4%B8%A4%E4%B8%AA%E5%8F%88%E4%B8%8D%E7%9B%B8%E7%AD%89%E4%BA%86%2C%E4%B8%BA%E4%BB%80%E4%B9%88%3F%E9%94%99%E4%BA%86%E5%93%AA%E9%87%8C%3F)
微积分问题:(xy)'=y'y'=(xy)' dy/dx=d(xy)/dx dy/dx=y+xdy/dx (1-x)dy/dx=y 1/ydy=1/(1-x)dx lny=ln|1-x|+C y=c(x-1)可代回去:y'=c (xy)=c(x^2-x) (xy)'=c(2x-1)两个又不相等了,为什么?错了哪里?
微积分问题:(xy)'=y'
y'=(xy)'
dy/dx=d(xy)/dx
dy/dx=y+xdy/dx
(1-x)dy/dx=y
1/ydy=1/(1-x)dx
lny=ln|1-x|+C
y=c(x-1)
可代回去:y'=c (xy)=c(x^2-x) (xy)'=c(2x-1)
两个又不相等了,为什么?错了哪里?
微积分问题:(xy)'=y'y'=(xy)' dy/dx=d(xy)/dx dy/dx=y+xdy/dx (1-x)dy/dx=y 1/ydy=1/(1-x)dx lny=ln|1-x|+C y=c(x-1)可代回去:y'=c (xy)=c(x^2-x) (xy)'=c(2x-1)两个又不相等了,为什么?错了哪里?
1/ydy=1/(1-x)dx 到下一步错了
应该是lny=-ln|1-x|+C
所以y=c/(1-x)
这里有隐函数求导的问题吧,遇到x就直接求导,遇到y,要先对y求导,再乘上y'或dy/dx,也就是(xy)'应该等于y+xy'
(xy)'=y'
xy=y+c
即可、。
y'=(xy)'=y+xy'
y'=y/(1-x)
y'/y=1/(1-x)
lny=ln|1-x|+C0
y=Ce^ln|1-x|
y=C|1-x|
x<1时,y=C-Cx
y'=-C (xy)=C(x-x^2) (xy)'=C(1-x)-Cx=y-(C-y)=-C
x>=1时同理