(x³ y³)dx-3xy²dy=0
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![(x³ y³)dx-3xy²dy=0](/uploads/image/f/16066-10-6.jpg?t=%28x%C2%B3+y%C2%B3%29dx-3xy%C2%B2dy%3D0)
解析2xdx+ydx+xdy+3y²dy=0(2x+y)dx+(x+3y²)dy=0(2x+y)dx=-(x+3y²)dydy/dx=(2x+y)/-(x+3y²
x^2*dy/dx=xy-y^2dy/dx=y/x-y^2/x^2u=y/xy=xuy'=u+xu'代入:u+xu'=u+u^2xu'=u^2du/u^2=dx/x-1/u=lnx+lnCCx=e^(
方法一(微分法)d(y/x)=d(ln(xy))(xdy-ydx)/x²=1/xy*d(xy)即(xdy-ydx)/x²=(ydx+xdy)/xy∴dy/dx=(xy+y²
两边求导(y'x-y)/x^2=(y+xy')/xyxy+x^2y'=xyy'+y^2y'=(xy-y^2)/(xy+x^2)
令z=1/x,则dx=-x²dz代入原方程得(x²y³+xy)dy=-x²dz==>dz/dy+y/x=-y³==>dz/dy+yz=-y³
ydx/dy+x=(e^x)(e^y)dx/dy+(e^x)(e^y)dx/dy=[(e^x)(e^y)-x]/[y-(e^x)(e^y)]dx/dy=(xy-x)/(y-xy)dx/dy=x(y-1
(6xy^2-y^3)dx+(6x^y-3xy^2)dy=d(3x^y^-xy^3),∴原式=(3x^y^-xy^3)|,=(9x^-7x)|=9*7-7=56.再问:原式==(3x^y^-xy^3)
答:dy/dx=1+x+y^2+xy^2y'=(1+x)(1+y^2)y'/(1+y^2)=1+x(arctany)'=1+x积分得:arctany=x+x²/2+Cy=tan(x+x
cos(x+y)(1+y')=y+xy'dy/dx=y'=[y-cos(x+y)]/[cos(x+y)-x]
令y/x=u,dy=u+xdu,原方程化为:u+xdu/dx=x/(u^2)+u,即du/dx=1/(u^2)通解为:y=x*[(3x+3c)^(1/3)]
dy=xy*dx+x*dx+y*dx两边同时积分y=y*1/2*x*x+1/2*x*x+xy(1-1/2*x*x-x)y=1/2*x*xy=x*x/(2-2x-x*x)+C*是乘号x*x是x的平方
∵dy/dx=(x+y^3)/(xy^2)==>xy^2dy=(x+y^3)dx==>y^2dy/x^3=dx/x^3+y^3dx/x^4(等式两端同除x^4)==>d(y^3)/(3x^3)+y^3
别人一般问一道题,你一下子5道?我给你个提示:1.所有5道题全部可以化成y'=f(y/x)的形式.比如5::y’=√(1-y^2/x^2)+y/x2.设y/x=uy=xuy'=u+xu',代入:u+x
令z=1/x,则dx=-x²dz代入原方程得(x²y³+xy)dy=-x²dz==>dz/dy+y/x=-y³==>dz/dy+yz=-y³
显然不是啊
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。
两边同时求导x+x(dy/dx)+1*(dy/dx)/y+1/x=0合并同类项dy/dx=-y/x
令y=xuy'=u+xu'代入方程:u+xu'=u^2/(u-1)xu'=u/(u-1)du(u-1)/u=dx/xdu(1-1/u)=dx/x积分;u-ln|u|=ln|x|+C1e^u/u=Cxe
你要求什么?