微分方程式xy`-2y=2x的通解是-搜答案-神马作文网

x^3(dy/dx)+2y^2=0x^3(dy/dx)=-2y^2y不为0时-dy/y^2=2dx/(x^3)两边同时积分得-1/y=1/x^2+cy=-1/(C+1/x^2)y=0时等式也成立

隐函数求导设z=x²y²-cos(xy)dy/dx=-(δz/δx)/(δz/δy)=-(2xy²+ysin(xy))/(2x²y+xsin(xy))=-y/x

-sin(xy)[ydx+xdy]=2xy^2*dx+x^2*2ydy-sin(xy)ydx-sin(xy)xdy=2xy^2*dx+2x^2*ydy-2x^2*ydy-sin(xy)xdy=2xy^

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)

2xdx+ydx+xdy+2ydy=0(x+2y)dy=-(2x+y)dxdy=-(2x+y)/(x+2y)×dx

令u=2x^2-y^2,v=xy然后链导法则!再问：请您把详细过程给我好吗？再答：偏导数符号打不上去啊du=(4xfu+yfv)dx+(-2yfu+xfv)dy其中fu、fv是偏导数符号

e^(-xy)-2z+e^z=0-ye^(-xy)-2z'(x)+e^zz'(x)=0z'(x)=ye^(-xy)/(e^z-2)-xe^(-xy)-2z'(y)+e^zz'(y)=0z'(y)=xe

分离变量法,很容易解的x^3/dx=-2y/dy两边积分,化简y=C1*exp(1/x^2)即y=C1*e^(1/x^2)再问：x^3(dy/dx)+2y^2=0打错了。。。再答：分离变量法，很容易解

y'+xy=x^3求微分

y'+xy=0的通解y.=Ce^(-x).特解y=x^2-2x.通解y=Ce^(-x)+x^2-2x.再问：不好意思啊，之前一直在忙别的。没有及时回复，首先谢谢你的回答。但是我觉得你的回答有点问题。‘

解；z(x)=2x+2y²z(y)=4xy+12y²dz=(2x+2y²)dx+(4xy+12y²)dy

∵x²dy+(y-2xy)dx=0==>x²dy/dx+(1-2x)y=0==>dy/y+(1/x²-2/x)dx=0==>ln|y|-1/x-2ln|x|=ln|C|(

x+2y=61式乘以2.2x+4y=123式2x+y=3k2式.3式减2式得3y=12-3k即y=4-k带入2式得x=2k-2由于x+y

dy/dx=3xy=xy^2dy/(3y+y^2)=xdx1/3*ln(y/3+y)=1/2*x^2+c1ln(y/3+y)=3/2*x^2+c2(c2=3c1)y/3+y=e^(3/2*x^2+c2

两边即对数得：lnz=xy*ln(lnu),不妨记u=x^2+y^2z'x/z=yln(lnu)+2x^2y/lnu,z'x=z[yln(lnu)+2x^2y/lnu]z'y/z=xln(lnu)+2

y=2^(x^2)的微分

y'=2^(x²)*ln2*(x²)'=2x*2^(x²)*ln2

隐函数求导的问题,由F(x,y)=0确定隐函数y=y(x),对方程两边求导时,其中含y的式子要始终注意y是一个x的函数,如(siny)'=cosy*y',(e^siny)'=e^siny*(siny)

原式两边微分2ydx+2xdy-2ydy=2dx故dy=(1-y)dx/(x-y)

y'=2e^2xcos(e^2x)把y看成复合函数sint,t=e^m,m=2x.复合函数求导,等于三个分别求导的积

dz=(y+1/y)dx+(x-x/y^2)dy