dy dx=2y x-y
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![dy dx=2y x-y](/uploads/image/f/552806-62-6.jpg?t=dy+dx%3D2y+x-y)
∵x2+y2-2x-4y+5=0,∴x2-2x+1+y2-4y+4=0,(x-1)2+(y-2)2=0,∴x=1,y=2,∴yx−xy=2-12=1.5;故答案为:1.5.
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
∵3x-5y=0,∴x=5y3,∴原式=5y3−2y5y3+3y=-111.
令y=ux则x^2(xdu+udx)/dx=2(ux)^2+ux^2约掉x^2(xdu+udx)/dx=2(u)^2+u所以(xdu)/dx=2(u)^2之后你该知道了吧求出u关于x的表达式再有y=u
∵(y^2+xy^2)dx+(x^2-yx^2)dy=0==>y²(1+x)dx+x²(1-y)dy=0==>[(y-1)/y²]dy=[(1+x)/x²]dx
2x+yx2-2xy+y2•(x-y)=2x+y(x-y)2•(x-y)(2分)=2x+yx-y;(4分)当x-3y=0时,x=3y;(6分)原式=6y+y3y-y=7y2y=72.(8分)
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
x=6-3y &nbs
∵1-8x≥0,8x-1≥0,∴x=18,y=12,∴代数式xy+yx+2-xy+yx−2=14+4+2-14+4−2=52-32=1.故选:B.
∵2lg(x-2y)=lgx+lgy∴lg(x-2y)2=lg(x•y),∴(x-2y)2=x•y,∴x2-5xy+4y2=0∴1-5•yx+4(yx)2=0解得yx=14,或yx=1(舍去)故答案为
似乎题目应该是y=√(x-2)+√(2-x)+4x-2>=02-x>=0x=2代入得y=4yx=4*2=8y的x次=4²=16
(1)x=4代入,4+y=4y-2y;所以y=4(2)y=4代入,4+4=4x-2*4;所以x=4
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).
xy+yx=10x+y+10y+x=11x+11y=100+x10x=100-11yx=10-1.1y所以y只能是0
∵x-y=4xy,∴2x+3xy-2yx-2xy-y=2(x-y)+3xyx-y-2xy=8xy+3xy4xy-2xy=112.故答案为:112.
yx+xy=x2+y2xy=(x+y)2-2xyxy当x+y=2,xy=-5时,原式=22-2×(-5)-5=-145.故答案为-145.
解答如下:x+2y=(yx)/44x+8y=xyxy-8y=4x(x-8)y=4x当x≠8时(x=8不成立)y=4x/(x-8)x+2y=(2x+1)/32y=(2x+1)/3-x2y=(1-x)/3
根号下则x-2>=0,x>=22-x>=0,x
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).