dx+ccnn+xyz

容哀飞957设函数z=z(x,y)由方程2xz+ln(xyz)=0确定,求dz/dx(详细步骤)设函数z=z(x,y),由方程e^z - xyz=a^3确定,求dz/dx -
冷馥宜19876995743 ______[答案] z=z(x,y) (1)2xz+ln(xyz)=0 (2)e^z-xyz=a^3 求:∂z/∂x=?记:z'=∂z/∂x1) 2z+2x(∂z/∂x)+[yz+xy(∂z/∂x)]/(xyz)=0z'(2x+1/z)=-2x-1/x=-(2x^2+1)/x解出:z' = -(...

容哀飞957sin(x+y)+e^xy=4 求y' -
冷馥宜19876995743 ______ 用微分法:两边求微分 cos(x+y)d(x+y)+e^(xy)d(xy)=0 cos(x+y)(dx+dy)+e^(xy)(xdy+ydx)=0 [cox(x+y)+ye^(xy)]dx+[cos(x+y)+xe^(xy)]dy=0 所以 y'=dy/dx=-[cox(x+y)+ye^(xy)]/[cos(x+y)+xe^(xy)]

容哀飞957(e^xsiny - xy^2)dx+(e^xcosy - x^2y+1)dy=0的通解 -
冷馥宜19876995743 ______ (e^xsiny-xy^2)dx+(e^xcosy-x^2y+1)dy=0的通解(e^xsiny-xy^2)dx+(e^xcosy-x^2y+1)dy=0(e^xsiny)dx-(xy^2)dx+(e^xcosy)dy-(x^2y)dy+dy=0(siny)d(e^x)+(e^x)dsiny-(xy^2)dx-(x^2y)dy+dy=0 d(e^xsiny)+dy-(xy^2)dx-(x^2y)dy=0 d(2e^xsiny)+d(2y)-(y^2)d(x^2...

容哀飞957(x^3+xy^2)dx+(x^2y+y^3)dy=0的通解,具体的解决步骤,一定要具体 -
冷馥宜19876995743 ______ 方程分离变量后两边积分得1/2ln(1+y^2)=1/2ln 1-x^2的绝对值+ln c1的绝对值.(x3 + xy2)dx + (x2y + y3)dy = 0 x(x2 + y2) + y(x2 + y2)dy/dx = 0(x2 + y2)(x + ydy/dx) = 0 x2 + y2 = 0 或 x + ydy/dx = 0 y dy = - x dx y2/2 = - x2/2 + C y2 = - x2 + C x2 + y2 = C 所以通解为x2 + y2 = 0 或 x2 + y2 = C 合并就是x2 + y2 = C

容哀飞957证明yz(2x+y+z)dx+xz(x+2y+z)dy+xy(x+y+2z)dz为全微分,并求原函数 -
冷馥宜19876995743 ______ 直接凑微分即可,yz(2x+y+z)dx=d(yzx^2+xzy^2+xyz^2)(这里y,z看成常数),同理xz(x+2y+z)dy=d(yzx^2+xzy^2+xyz^2),xy(x+y+2z)dz=d(yzx^2+xzy^2+xyz^2),所以当把x,y,z都当做变量时,这个微分表达式=d(yzx^2+xzy^2+xyz^2),因此是全微分,其原函数就是yzx^2+xzy^2+xyz^2.

容哀飞957求有方程xy+siny+e^2=0所确定的隐函数的导数dy/dx -
冷馥宜19876995743 ______[答案] xy+siny+e^2=0 xdy/dx + y + cosy dy/dx =0 dy/dx = -y/(x+cosy)

容哀飞957du(x,y)=2xycos(x^2y)dx+x^2cos(x^y)dy,求u(x,y) -
冷馥宜19876995743 ______[答案] 因为du/dx=2xycos(x^2y)所以u(x,y)=∫2xycos(x^2y)dx=∫cos(x^2y)d(x^2y)=sin(x^2y)+A(y) 其中A(y)是关于y的任意函数因为du/dy=x^2cos(x^2y)所以x^2cos(x^2y)+A'(y)=x^2cos(x^2y)所以A'(y)=0A(y)=C所以u(x,y)=sin(x^...

容哀飞957由x+y+z=根号下xyz,确定z是x,y的函数,求dz -
冷馥宜19876995743 ______[答案] d(x+y+z)=d√(x+y+z)dx+dy+dz=1/2√(xyz) d(xyz)dx+dy+dz=1/2√(xyz) (yzdx+xzdy+xydz)(1-xy/(2√xyz))dz=[yz/(2√xyz)-1]dx+[xz/(2√xyz)-1]dydz=[yz/(2√xyz)-1]/(1-xy/(2√xyz))dx+[xz/(2√xyz)-1]/(1-xy/(2√x...

容哀飞957求微分通解 dy/dx=(1+y^2)/(xy+x^3y) -
冷馥宜19876995743 ______[答案] dy/dx=(1+y^2)/(xy+x^3y) dy/dx=(1+y^2)/[y(x^3+x)] ydy(x^3+x)=(1+y^2)dx ydy/(1+y^2)=dx/(x^3+x) 1/2∫1/(1+y^2)d(1+y^2)=1/2∫[1/x^2-1/(x^2+1)]d(x^2) ∫1/(1+y^2)d(1+y^2)=∫1/x^2d(x^2)-∫1/(x^2+1)d(x^2+1) ln(1+y^2)=lnx^2-ln(x^2+1) ln(1+y^2)=ln(x^2/(x^2+1))+...

容哀飞957(2x+xy^2)dx+(2y+x^2*y)dy=0 -
冷馥宜19876995743 ______ 解:∵(2x+xy^2)dx+(2y+x^2*y)dy=0 ==>(xy^2dx+x^2*ydy)+(2xdx+2ydy)=0 ==>d(x^2*y^2)+2d(x^2+y^2)=0 ==>x^2*y^2+2(x^2+y^2)=C (C是常数) ∴原方程的通解是x^2*y^2+2(x^2+y^2)=C.