xy=e~x y秋dy dx-搜答案-拍题作业网

e(-xy)d(-xy)=(xdy+ydx)d(exy^2/2)=d(xy)exy^2=2xy+C,C为任意常数,或x恒等于0,或y恒等于0,或x和y都为常数不知道有没有错呢···

方程两边求关x的导数ddx(xy)＝(y+xdydx)； ddxex+y＝ex+y(1+dydx)；所以有（y+xdy

方程两边对x求导,得：y+xy'+y'e^y=2y+2xy'y'e^y-xy'=y得y'=y/(e^y-x)因此dy=ydx/(e^y-x)

dy/dx=e^(xy)dy/e^y=e^xdx两边积分得-e^(-y)=e^x+C再问：你这样右边是e^(x+y)啊再答：噢令xy=p两边求导得y+xy'=p'y'=(p'-y)/x=(p'-p/x

对方程取导数y+x(dy/dx)+(dy/dx)=0(dy/dx)(x+1)=-ydy/dx=(-y)/(x+1)

xy'=y+xy的

xdy=(y+xy)dxdy/y=((1+x)/x)dxln|y|=ln|x|+x+cy=±e^(ln|x|+x+c)其中c是常数再问：真还不理解我们是选择题：y=cxe^xy=c+x-x^2y=cs

xy=e^(x+y),求dx/dy

ydx/dy+x=(e^x)(e^y)dx/dy+(e^x)(e^y)dx/dy=[(e^x)(e^y)-x]/[y-(e^x)(e^y)]dx/dy=(xy-x)/(y-xy)dx/dy=x(y-1

该题为隐函数求导.xy+e^(xy)=1则y+xy'+e^(xy)(y+xy')=0解得：y'=-y/x解答完毕.

两端对x求导得y+xy'=e^(xy)*(y+xy')整理即可得dy/dx=y再问：y'=y+e^xy/e^xy-x?再答：是的啊，就是这样啦。

两边求导：e^(xy)*(xy)'-(xy)'=0e^(xy)*(y+xy')-(y+xy')=0ye^(xy)+xe^(xy)*y'=y+xy'x(e^(xy)-1)y'=y(1-e^(xy))y'

两边同时求导..得：y-e^xy(yx')=0x'=y/(ye^xy)所以dy/dx=y/(ye^xy)

这是一阶线性微分方程，其中P（x）=1，Q（x）=e-x∴通解y＝e−∫dx(∫e−x•e∫dxdx+C)＝e−x(∫e−x•exdx+C)＝e−x(x+C)．

你好!两边对x求导：e^(xy)*(y+xy')-y^2=y'cosy解得y'=(y^2-ye^(xy))/(xe^(xy)-cosy)

7=xy-e^(xy),求dy/dx

如图.

就是方程两边的每一项都对x进行求导,这里要将y看成是复合函数,y=y(x)比如x对x求导,则为1对y求导,则为y'对xy求导,应用求导运算法则,为y+xy'

x+y=e^xy 求导y`=?

思路：x+y=e^xy,两边取微分d(x+y)=d(e^xy)dx+dy=e^xyd(xy)dx+dy=e^xy(xdy+ydx)dx+dy=xe^xydy+ye^xydx(xe^xy-1)dy=(1

两边求导得y'·e^y+(y+xy')/(xy)+e^(-x)=0

答：xy=x-e^(xy)e^(xy)=x-xy=x(1-y)两边对x求导：(xy)'e^(xy)=1-y-xy'(y+xy')e^(xy)=1-y-xy'ye^(xy)+xy'e^(xy)+xy'=

在方程ex+y+cos（xy）=0左右两边同时对x求导，得：ex+y（1+y′）-sin（xy）•（y+xy′）=0，化简求得：y′＝dydx＝ysin(xy)−ex+yex+y−xsin(xy)．