8x y=k 1 x 8y=3
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x2-xy=-3①,2xy-y2=-8②,①×2+②×3得:2x2-2xy+6xy-3y2=-6-24=-30,则2x2+4xy-3y2=-30.
1.2(Xy+Xy)-3(Xy-xy)-4Xy=2*2xy-0-4xy=4xy-4xy=02.1/2ab-5aC-(3acb)+(3aC-4aC)=1/2ab-5ac-3acb-ac=1/2ab-6a
(-3x^y+2xy)-(4x^+xy)=-3x^y+2xy-4x^-xy=-3x^y+xy-4x^所以填上-3x^y+xy-4x^
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
3xy-[2xy-2(xy-2分之3xy)+xy]+3xy=6xy-[2xy-2xy+3xy+xy)=6xy-4xy=2xy=2×3×3分之1=2
(8xy-3x平方)-5xy-2(3xy-2x平方)=8xy-3x²-5xy-6xy+4x²=x²-3xy=4+6=10
1、已知2x²+xy=10,3y²+2xy=6,求4x²+8xy+9y²的值为?分析:通过观察,可以把8xy拆成2xy+6xy,分别于剩余的两项组合,并提取公因
不含xy项就是说含XY的项为0即3kxy+三分之一xy=0解得K=-(1/9)
(3x^2+2xy)/xy-(2x^2-xy)/xy=(3x^2+2xy-2x^2+xy)/xy=(x^2+3xy)/xy=x(x+3y)/xy=(x+3y)/y
就是把这dydx转为求导前的式子,然后再求导一遍验证一下对错.再问:就是算到最后有个积分搞不出来。求过程。
设X=kY.kY^2/(3k+2)Y=1/8kY^2/((2k+3)Y=1/7由上式得:3k+2=8kY,2k+3=7kY所以2/(8Y-3)=3/(7Y-2)所以Y=1/2,X=1
(5xy+4x+7y)+(6x-3xy)-(4xy-3y)=5xy+4x+7y+6x-3xy-4xy+3y=(5xy-3xy-4xy)+(4x+6x)+(7y+3y)=-2xy+10x+10y=-2x
x²-3kxy+1/3xy-8=x²+(1/3-3k)xy-8所以1/3-3k=0k=1/9
dx/dy-3xy=xy^2dx/x=(y^2+3y)dy两边积分得:lnx=y^3/3+3y^2/2+c==>x=exp(y^3/3+3y^2/2+c)=Cexp(y^3/3+3y^2/2)C常数
∵A=8x²y-6xy²-3xy,B=7xy²-2xy+5x²y ∴C=3(A+B) =3(8x²y-6xy²-3xy+7xy²
X+y=3xy=-5X-y=?(x-y)^2=(X+y)^2-4xy=9+20=29则x-y=±根号29
-2x的平方-12xy的2次方+8xy的3次方=-2x(x+6y²-4y³)
由xy+x=16,得x=16/(y+1)代入xy-x=8,得16y/(y+1)-16/(y+1)=8=>16(y-1)/(y+1)=8=>(y-1)/(y+1)=1/2移项,通分得y-3/2(y+1)
dy/dx=xy²+3xydy/dx=x(y²+3y)∫1/[y(y+3)]dy=∫xdx(1/3)∫(3+y-y)/[y(y+3)]dy=∫xdx∫[1/y-1/(y+3)]dy