(y^2-2xy)dx+x^2dy=0 齐次微分方程!麻烦大虾们帮个忙啊

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(y^2-2xy)dx+x^2dy=0 齐次微分方程!麻烦大虾们帮个忙啊
(y^2-2xy)dx+x^2dy=0 齐次微分方程!
麻烦大虾们帮个忙啊

(y^2-2xy)dx+x^2dy=0 齐次微分方程!麻烦大虾们帮个忙啊
令：v=y/x,y=xv,dy=vdx+xdv
dy/dx = -(y^2-2xy)/x^2
(vdx+xdv)/dx = 2v - v^2
v+xdv/dx = 2v - v^2
xdv/dx = v - v^2
dv/[v(1 - v)] = dx/x
∫dv/[v(1 - v)] = ∫dx/x
∫dv/v + ∫dv/(1 - v)] = ∫dx/x
lnv - ln(1-v) = lnx
ln(v/(1-v))=lnx+lnc
v/(1-v)=cx
(y/x)/(1-(y/x))=cx
y/(x-y)=cx
y=cx(x-y)

求解微分方程 x^2*dy/dx=xy-y^2 求齐次微分方程dy/dx=y^2/xy-x^2 dy/dx=xy/x^2-y^2 dy/dx=1+x+y^2+xy^2 求通解:(xy-x^2)dy=y^2dx 微分方程求解 (x^2y^3+xy)dy=dx 解微分方程 (x^2y^3+xy)dy=dx x^2+xy+y^3=1,求dy/dx dy/dx=(x+y^3)/(xy^2) 微分方程求解 (x^2y^3+xy)dy=dx dy/dx=(x+y^3)/xy^2 常微分方程dy/dx=(x^3+xy^2)/y dy/dx=y^2/(x-xy)是齐次方程吗 y/x=ln(xy) 求dy/dx(xy-y^2)/(xy+x^2) （xy-y^2)dx-(x^2-2xy)dy=0微分方程通解 1.求（xy^2+x）dx+（xy^2-y）dy=0的通解微分方程 xy-1/x^2y dx - 1/xy^2 dy =0 1.dy/dx=(y-x)/(y+x)2.x^2*dy/dx=xy-y^2