Solve (y+x3y+2x2)dx+(x+4xy4+8y3)dy=0 https://math.stackexchange.com/questions/2590017/solve-y-x3y-2x2dx-x-4xy4-8y3dy-0 (y+x3y+2x2)dx+(x+4xy4+8y3)dy=0 ⇒(ydx+xdy)+x3ydx+(2x2dx)+4xy4dy+(8y3...
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(n+3) 对比系数项得4n-2m=0,3n-5m+7=0,有解n=1,m=2.即积分因子为 μ=x^2y .方程乘积分因子后为4x^3y^2dx+3x^2y^5dx+2x^4ydy+5x^3y^4dy=d(x^4y_1^2)+d((x^3 .求得方程的积分式为x^4y^2+x^3y^5=c 和x=0,y=0.解2应用[书习题2.3-7∃:(δM)/(δy)-(θN)/(δx)=...
方程可以化为 dy/dx = 3y/x 设y/x = u 有 du = (xdy-ydx) /x^2 整理有 du/dx = (xdy/dx -y )/x^2 x* du/dx +y/x =dy/dx 即 xdu/dx +u =dy/dx 代入我的第一行原方程 有xdu/dx +u = 3u 再整理有 du/u=2dx/x 得到u=Cx^2 C为常数 即y/x =Cx^2 , y =...
解：∵(3xy+x^2)dy+(y^2+xy)dx=0==>2y(3xy+x^2)dy+2y(y^2+xy)dx=0(等式两端同乘2y)==>2(3xy^2dy+y^3dx)+2(x^2ydy+xy^2dx)=0==>2d(xy^3)+d(x^2y^2)=0==>2∫d(xy^3)+∫d(x^2y^2)=0==>2xy^3+x^2y^2=C(C是常数)∴此方程的通解是2xy^3+x^2y^2...
du=2dx+3dy,dy=(xdy+ydx)e^xy偏导数符号打不出来.用p代替吧,dz=(pz/pu)du+(pz/pv)dv=(pz/pu)(2dx+3dy)+(pz/pv)(xdy+ydx)e^xy=[2pz/pu+ye^xy pz/pv]dx + [3pz/pu+xe^xy pz/pv]dy 21834 设函数y=f(x)的图像上点(0,-2)处切线为2x-3y=6则此函数可能为___ 2x-3y=6可化为...
1+2x)1、z=(1+x)^ylnz = yln(1+x)(1/z)dz = ln(1+x) dy + [y/(1+x)].dydz = { ln(1+x) dy + [y/(1+x)].dy} .(1+x)^y 2、dz=xdx+ydy。z=xy，那么dz自然而然等于dxy；dz=(ðz/ðx)dx+(ðz/ðy)dy；=ydx+xdy。3、...
微分方程ydx+xdy=0的通解是() A 找粽子礼盒团购,上阿里巴巴 粽子礼盒团购从原料,生产,加工一系列服务.找阿里巴巴,全球领先采购批发平台!广告 求微分方程y^2dx+(x^2+xy)dy=0 的通解 x/y=udx=ydu+udyy^2dx+(x^2+xy)dy=0dx+[(x/y)^2+(x/ 微分方程y"+8y'+16y=0通解为? 的通解:y=(C1+C2x)...
dz=f(xy,x+3)dy+y[f1''(ydx+xdy)+f2''(dx+3dy)] =f(xy,x+3)dy+f1''y2dx+xyf1''dy+yf2''dx+3yf2''dy =(f1''y2+yf2'')dx+[f(xy,x+3y)+xyf1''+3yf2'']dy 即: ? z/? x=f1''y2+yf2'', ? z/? y=f(xy,x+3y)+xyf1''+3yf2'', ...
两边对y求偏导数得:cosz — xz xy — 0 yy 解得:-Jy cos z xy 七、求旋转抛物面z 2x22y2 解:由全微分方程的不 变性,得 dz—du—dv u v evdu uevdv exyd (x2y2) (x2y2)exyd(xy) exy(2xdx 2ydy) (x2y2)exy(ydx xdy) xy23xy,32、, e (2x x y y )dx e (x 2y xy )dy...