e的xy次方求微分dy

谢看郑1142xy^2+e^y=0,求在(0,0)微分dy -
厍念迫13325162266 ______[答案] 两边求微分,得 d(xy^2+e^y)=0 d(xy^2)+d(e^y) y^2dx+xdy^2+e^ydy=0 y^2dx+2xydy+e^ydy=0 (2xy+e^y)dy=-y^2dx dy=-y^2/(2xy+e^y) dx

谢看郑1142求隐函数xy等于e的x+y次方的微分dy -
厍念迫13325162266 ______[答案] Y+xY'=e^(X+Y)*(1+Y') Y'(x-e^(X+Y))=e^(X+Y)-Y dy=[e^(X+Y)-Y]/[(x-e^(X+Y))]*dx

谢看郑1142y'=e的x - y次方怎么做,求微分, -
厍念迫13325162266 ______[答案] 解微分方程吧 y'=e^(x-y) dy/dx=e^x/e^y e^ydy=e^xdx e^y=e^x+c y=ln(e^x+c)

谢看郑1142Y' - 2Y=E的X次方.求微分方程的通解 -
厍念迫13325162266 ______[答案] dy/dx-2y=e^x(1)先求齐次微分方程dy/dx-2y=0的通解.该方程的特征根满足λ-2=0,得λ=2故齐次微分方程通解y=Ce^(2x)(2)再求非齐次微分方程特解.定义微分运算d/dx=D,1/D=∫,本式中L(D)=D-2,则特解y*有(D-2)y*=e^x.故y*=...

谢看郑1142求下列函数的微分dyy=tan(e的x次方) -
厍念迫13325162266 ______[答案] y'=[sec(e^x)]^2*(e^x)' =e^x*[sec(e^x)]^2 所以dy=e^x*[sec(e^x)]^2dx

谢看郑1142z=e的xy次方cosxy求全微分 -
厍念迫13325162266 ______[答案] dz=Zxdx+Zydy Zx=ye^xy*cosxy+e^xy*-ysinxy Zy=xe^xy*cosxy+e^xy*-xsinxy dz=(ye^xy*cosxy+e^xy*-ysinxy)dx+(xe^xy*cosxy+e^xy*-xsinxy)dy

谢看郑1142求微分方程e的(x - y)次方dx - dy=0的通解,请求数学达人给出详细步骤大神们帮帮忙 -
厍念迫13325162266 ______[答案] e^(x-y)dx-dy=0 即e^(x-y)dx=dy 即e^xdx=e^ydy 两边分别积分,得 e^x+C=e^y 即为通解 对上式两边对x求导好象还是e的(x-y)次方dx-dy=0

谢看郑1142设y等于y(x)是由方程e的x次方减e的y次方等于sin(xy)所确定的隐涵数求微分dy
厍念迫13325162266 ______ e^x-y'e^y=cos(xy)y' y'=e^x/(cos(xy)+e^y) dy=e^x/(cos(xy)+e^y)dx

谢看郑11421+y'=e的y次方,求微分方程的通解! -
厍念迫13325162266 ______[答案] 1+dy/dx=e^y dx+dy=e^y*dx dy/(e^y-1)=dx [-1+e^y/(e^y-1)]dy=dx 左边对y进行积分,右边对x进行积分,得 -y+ln(e^y-1)=x+c

谢看郑1142y'=e的2x - y次方 y(0)=0 求这个微分方程满足初始条件的特解 -
厍念迫13325162266 ______[答案] y'=e的2x-y次方 dy/dx=e的2x次方*e的-y次方 e的y次方*dy=e的2x次方dx e的y次方=1/2*e的2x次方+c 带入y(0)=0得,c=1/2