(x xy^2)dx-(x^2y y)dy=0

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d^2y/dx^2=(dy/dx)'×(dy/dx),另外请解释下dx,dy的含义,dx和dy是指x=...和y=...

不对,d^2y/dx^2是二阶导的意思,不是乘方.dy/dx是一阶导,相当于f’

dy/dx,y=(1+x+x^2)e^x

dy/dx=(1+x+x²)'*e^x+(1+x+x²)*(e^x)'=(1+2x)e^x+(1+x+x²)e^x=(2+3x+x²)e^x

d/dx((x^2+y^2)^2)=d/dx(x^2-y^2),求(化简)dy/dx=?

求导得:2(x^2+y^2)(2x+2yy')=2x-2yy'x-2x(x^2+y^2)=(2y(x^2+y^2)+y)y'y'=[x-2x(x^2+y^2)]/(2y(x^2+y^2)+y)

微分方程dy/dx=y/(x+y^2)的通解?

设t=x/y则x=tydx=tdy+ydtdy/dx=y/(x+y^2)=>dx/dy=x/y+y把dx代入t+ydt/dy=t+yydt/dy=ydt/dy=1t=y+C(C是常数)x=y^2+Cy

微分方程 dy/dx=(-2x)/y

ydy=-2xdx积分y²/2=-x²+C'所以y²=-2x²+C

y=2x^2+x求dy/dx

dy=d2x²++dxdy=2xdx+dx所以dy/dx=2x+1

2*x*y^2(dy/dx)- x^3(dy/dx)=2y^3

∵2xy²dy/dx-x³dy/dx=2y³==>(2xy²-x³)dy/dx=2y³∴dx/dy=x/y-x³/(2y³

微分方程 dy/dx=y-(2x)/y

其实很简单,楼主需要把微分和积分合起来玩,不要玩一个!设y=f(x),则dy/dx就为f(x)的导数y',同理dy^2/dx就是y^2对x的导数,即(y^2)'=2y*y'=2y*dy/dx,(y^2

dy/dx=x(1+y^2)/y通解

ydy/(1+y^2)=xdxd(y^2)/(1+y^2)=2xdx积分:ln(1+y^2)=x^2+C11+y^2=Ce^(x^2)

解方程y^2+x^2*(dy/dx)=x*y*(dy/dx)

dy/dx=y^2/(xy-x^2)=(y/x)^2/(y/x-1),令u=y/x,则dy/dx=u+xdu/dx,方程变成u+xdu/dx=u^2/(u-1),接下来可以自己完成,把u移到右侧用分离

dy/dx=2y/x+3x/2y

令y/x=zdy/dx=dz/dx*x+z带入原方程2z/(2z^2+3)dz=1/xdx两边积分就可以算出来了1/2ln(2z^2+3)lnx+c再把y/x=z带入上市就可以了

dy/dx=x/2y dy/dx=x+y

dy/dx=x/2y2ydy=xdx两边同时积分得:y^2=x^2/2+C(C为常数)dy/dx=x+y令t=x+y则dt/dx=1+dy/dx原式转化为:dt/dx-1=tdt/dx=t+1dt/(

dy/dx-y/x=x^2

这是一阶常微分方程1、通解部分dy/dx-y/x=0dy/y=dx/x两边积分lny=lnx+cy=cx2、求特解y=x*M(x)dy/dx=M(x)+x*M'(x)dy/dx-y/x=2x^2M(x

(x^2)dy+(y^2)dx=dx-dy

(x^2+1)dy=(1-y^2)dxdy/(1-y)(1+y)=dx/(x^2+1)1/2lnl(y-1)/(y+1)l=arctanx+c再问:在帮我一个,我给再加五分,y′=y,y(0)=1.谢

dy/dx-2y/(x+1)=(x+1)^2

∵dy/dx-2y/(x+1)=0==>dy/y=2dx/(x+1)==>ln|y|=2ln|x+1|+ln|C|(C是积分常数)==>y=C/(x+1)²∴设原方程的通解为y=C(x)/(

微分方程dx/2(x+y^4)=dy/y

解法一:(全微分法)∵dx/2(x+y^4)=dy/y==>ydx=2(x+y^4)dy==>ydx-2xdy=2y^4dy==>(ydx-2xdy)y³=2ydy==>d(x/y²

dy/dx+(e^((y^2)+x))/y=0

dy/dx=-[e^(y^2)*e^x]/y-ye^(-y^2)dy=e^xdx∫-ye^(-y^2)dy=∫e^xdx1/2*∫e^(-y^2)d(-y^2)=∫e^xdxe^(-y^2)=2e^x

求dy/dx=x/y+(cosx/y)^2通解

求dy/dx=(x/y)+cos²(x/y)通解令x/y=u,则y=x/u,dy/dx=[u-x(du/dx)]/u²,代入原式得:[u-x(du/dx)]/u²=u+c

求dy/dx=(x-y+5)/(x+y-2)

dy/dx=(x-y+5)/(x+y-2)=[(x+3/2)-(y-7/2)]/[(x+3/2)+(y-7/2)]令v=y-7/2,u=x+3/2,原方程化为dv/du=(u-v)/(u+v)变为齐次

d^2y /dx^2 - 24 =0 dy/dx -2y = e^-x

再问:想知道最后一题公式谢谢再答:第三个和第二个用的同一个公式啊