y^3 y^2=2x ,求dy dx

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

2/3

(2x-y)/(x+y)=3所以(x+y)/(2x-y)=1/3原式=1/2*(2x-y)/(x+y)+1/3*(x+y)/(2x-y)=3/2+1/9=29/18

方程两边对x求导得2x+y′x2+y＝3x2y+x3y′+cosxy′＝2x−(x2+y)(3x2y+cosx)x5+x3y−1由原方程知，x=0时y=1，代入上式得y′|x＝0＝dydx|x＝0＝1

2x-y/x+3y=2得x+3y/2x-y=1/24x-2y/x+3y减4x+12y除以2x-y=2(2x-y)/x+3y-4(x+3y)/2x-y=2乘以2-4乖以1/2=4-2=2

3x=8yx/y=8/3（1）x+y/y=x/y+1=8/3+1=11/3(2)2x+3y/x-2y分子分母同时除以y得=(2x/y+3)/(x/y-2)=(16/3+3)/(8/3-2)=(25/3

∵2x-y/x+2y=3∴2(2x-y)/x+2y-9(x+2y)/2x-y+3＝2×3-9×1/3+3=6

答案是2.4x-2y/x+3y=(2x-y/x+3y)乘以2=4,4x+12y/2x-y=(x+3y/2x-y)乘以4=1/2x4=2,所以代数式等于4-2=2.

X+Y分之X-Y等于3x=-2yX+Y分之2(x-y)减X+Y分之3X+Y=(-x-3y)/(x+y)=1

x+y分之x-y=2求x+y分之3x-3y减x-y分之2(x+y)的值x+y分之x-y=2x-y=2(x+y)(x+y)分之(3x-3y)-(x-y)分之2(x+y)的值x+y分之3x-3y=(x+y

因为(x-y)/(x+y)=3,则(x＋y)/(x－y)＝1/3则5(x-y)(x+y)-(x+y)/2(x-y)＝5*3-1/(3*2)=15-1/6=89/6

3x^2+xy-2y^2=0推出(3x-2y)(x+y)=0推出x=-y或x=(2/3)y{(x+y)/(x-y)+4xy/(y^2-x^2)}/{(x+3y)*(x-y)}/x^2-9y^2推出：{

（x+y)（x-y)-y^2+（x-y)^2-（6x^2y-2xy^2)÷2y=（x+y)（x-y)-y^2+（x-y)^2-2y（3x^2-xy)÷2y=（x+y)（x-y)-y^2+（x-y)^2

即y/x=2arctan(y/x)令u=y/x,则u=2arctanu这实际是一个关于u的方程,可以证明这个方程是有解的,设u=c是方程的解(这时c已经是一个常数了)即u=y/x=c那么有y=cx所以

y'=(cos²x)'-(sin3^x)'=2cosx·(cosx)'-cos3^x·(3^x)'=2cosx·(-sinx)-cos3^x·(3^x·ln3)=-sin2x-ln3·cos

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)．

2x-y\x+y=32x-y=3(x+y)2x-y=3x+3y3x-2x=-y-3yx=-4y2x-y/2x+2y+x+y/6x-3y=(-8y-y)/(-8y+2y)+(-4y+y)/(-24y-3

(x-2y)/(x+2y)=3取倒数(x+2y)/(x-2y)=1/3所以原式=(1/3)[(x-2y)/(x+2y)]-3[(x+2y)/(x-2y)]=(1/3)×3-3×(1/3)=0

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)．

原式=x-x+x-x+……-x+(2-1+4-3+5-4+……+2008-2007-2009）y=0+(1×1004-2009)y=-1005y=1005/2