(1-x^2)dy/dx+xy=1
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/27 11:46:23
(1-x^2)dy/dx+xy=1(1-x^2)dy/dx+xy=1(1-x^2)dy/dx+xy=1∵(1-x^2)dy/dx+xy=1==>(1-x^2)dy+xydx=dx==>dy/(1-x^
(1-x^2)dy/dx+xy=1
(1-x^2)dy/dx+xy=1
(1-x^2)dy/dx+xy=1
∵(1-x^2)dy/dx+xy=1
==>(1-x^2)dy+xydx=dx
==>dy/(1-x^2)^(1/2)+xydx/(1-x^2)^(3/2)=dx/(1-x^2)^(3/2) (等式两端同除(1-x^2)^(3/2))
==>dy/(1-x^2)^(1/2)+yd(1/(1-x^2)^(1/2))=dx/(1-x^2)^(3/2)
==>d(y/(1-x^2)^(1/2))=d(x/(1-x^2)^(1/2))
==>y/(1-x^2)^(1/2)=x/(1-x^2)^(1/2)+C (C是常数)
==>y=x+C(1-x^2)^(1/2)
∴原方程的通解是y=x+C(1-x^2)^(1/2).
(1-x^2)dy/dx+xy=1
dy/dx=1+x+y^2+xy^2
x^2+xy+y^3=1,求dy/dx
differential equation:x^2 dy/dx + xy = 1
微分方程 xy-1/x^2y dx - 1/xy^2 dy =0
求方程(x*x+1)dy/dx+2xy=4x*x的通解.
dy/dx 求导 (x^2-(xy)^1/2+y^2)=53(x^2-(xy)^1/2+y^2)=53的dy/dx 谢谢!
dx/dy+xy=-1,求通解
dy/dx=xy-1 奇葩无比...
(x^2+1)dy/dx+2xy=4x^2
e^xy+x+y=2求dy/dx |x=1
求(xy^2+x)dx+y(1+x^2)dy=0的通解
齐次方程求通解问题(y^2)dx+(x^2-xy)dy=0 求通解我的解:(y^2)dx+(x^2)dy-(xy)dy=0 (y^2)dx+(x^2)dy=(xy)dy[(y^2)dx/(xy)dy]+[(x^2)dy/(xy)dy]=1得 (ydx/xdy)+(x/y)=1令u=y/x 则dx/dy=（1-1/u）/u dy/dx=u/(1-1/u) 我这么算 正确答案分子
dy/dx=(x+1)^2+(4y+1)^2+8xy+1 求通解
急求微分方程（1+x ^2）dy=（1+xy）dx 的通解
高数微分方程 dy/dx=(1+xy)/(1+x^2)
求dy/dx=1-x+y^2-xy^2的通解
设X^2+Y^2-XY=1,求dy/dx