2dy−dx=(dx−dy)ln(x−y)+(x−y)× 1 x−y (dx−dy) 2dy-dx=(dx-dy)ln(x-y)+dx-dy [3+ln(x-y)]dy=[2+ln(x-y)]dx (x-y)[3+ln(x-y)]dy=(x-y)[2+ln(x-y)]dx [3(x-y)+(x-y)ln(x-y)]dy=[2(x-y)+(x-y)ln(x-y)]dx 因为2y-x=(x-y)...
三、 求隐函数或参数方程决定函数的导数:(1 y=y(x)由方程 x^2y+e^y=ln "决定 ,求 (dy)/(dx) (2)y=y(x)由参数方程确定,求y=3e"-4e+7 相关知识点: 试题来源: 解析 解: x^2y+e^y=lnx⇒2xy+x^2(dy)/(dx)+e^y(dy)/(dx)=1/x⇒(dy)/(dx)=(1-2x^2y)/ 解: ...
2、设f(x)在〔0,1〕上可导,且0 答案 第一题,这是个隐函数,两边对x求导得:2y'-1=(1-y')*ln(x-y)+(x-y)*(1-y')/(x-y)=(1-y')*ln(x-y)+(1-y')所以[3+ln(x-y)]y'=ln(x-y)+2y'=[ln(x-y)+2]/[ln(x-y)+3]所以dy=[ln(x-y)+2]dx/[ln(x-y)+3]第二题,...
简单分析一下，答案如图所示
简单分析一下，答案如图所示
【题目】方程\(x=lnsint^2y=cost+tsint. 确定y为x的函y= cos t+ tsin t数求 (dy)/(dx) (d^2y)/(dx^2)
1.求下列可分离变量的微分方程的通解(1)(dy)/(dx)=\frac(x^2y (2) (dy)/(dx)=ylnx ;(3)) (dy)/(dx)=y^2cosx
因为2y-x=(x-y)ln(x-y),所以,[3(x-y)+(2y-x)]dy=[2(x-y)+(2y-x)]dx(2x-y)dy=xdx①若2x-y=0,则dy=2dx② 若2x−y≠0,则dy= x 2x−ydx; 直接求微分,然后移项即可. 本题考点:复合函数微分法则. 考点点评:本题考查函数微分的求解.需要①注意变量的关系;②全部求微分后要进行化简....
1.求y'-2y＝0的通解 解：∵y'-2y＝0 ==>dy/dx=2y ==>dy/y=2dx ==>ln│y│=2x+ln│C│ (C是积分常数)==>y=Ce^(2x)∴原方程的通解是y=Ce^(2x) (C是积分常数)。2.求y'＝y/(y-x)的通解 解：∵令y=xt，则y'=xt'-t 代入原方程，得xt'-t=t/(t-1)==>xt'=t...
2y-x=(x+y)ln(x-y)两边微分可得：2y'-1=(1+y')ln(x-y)+(x+y)【（1-y')/(x-y)】之后就是化简了,将y’放在一边,其余的放在另一边.