神马作文网(y^2-2xy)dx+x^2dy=0 齐次微分方程!
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/13 13:01:04
(y^2-2xy)dx+x^2dy=0 齐次微分方程!
麻烦大虾们帮个忙啊
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)
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)
(y^2-2xy)dx+x^2dy=0 齐次微分方程!高手进阿
(y^2-2xy)dx+x^2dy=0 齐次微分方程!
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
解微分方程 (x^2y^3+xy)dy=dx
微分方程求解 (x^2y^3+xy)dy=dx
解微分方程y^2+(x^2)(dy/dx)=xy(dy/dx)
（xy-y^2)dx-(x^2-2xy)dy=0微分方程通解
微分方程 xy-1/x^2y dx - 1/xy^2 dy =0
微分方程（xy-y）dy-(x+xy^2)dx=0的通解是?
求解一个微分方程：（2x·y^2-y)dx+(y^2+xy)dy = 0
求微分方程(xy^2-x)dx+(x^2y+y)dy=0的通解