求微分方程的通解(3x눀-y눀)dy-2xydx=0

求微分方程的通解(3x눀-y눀)dy-2xydx=0求过程,谢谢
2024-11-22 17:39:03
推荐回答(2个)
回答1:

dy/dx=2(y/x)/(3-(y/x)²)
令u=y/x,dy/dx=u+xdu/dx
xdu/dx=2u/(3-u²)-u
(3-u²)/(u³-u)du=dx/x
1/(u-1)-3/u+1/(u+1)du=lnx+lnC
(u²-1)/u³=Cx
(y²x-x³)/y³=Cx
y²-x²=Cy³

回答2:

(3x²-y²)y'=2xy