分离变量
xydy/dx=1-y^2
ydy/(1-y^2)=dx/x
两边积分
∫ydy/(1-y^2)=∫dx/x
左边用变量替换t=1-y^2
dt=-2ydy
ydy=(-1/2)dt
所以
∫(-1/2)dt/t=ln|x|
(-1/2)ln|1-y^2|+C=ln|x|
|x|=Cexp((-1/2)ln|1-y^2|)
|x|=C(|1-y^2|)^(-1/2)
分离变量
xydy/dx=1-y^2
ydy/(1-y^2)=dx/x
两边积分
∫ydy/(1-y^2)=∫dx/x
左边用变量替换t=1-y^2
dt=-2ydy
ydy=(-1/2)dt
所以
∫(-1/2)dt/t=ln|x|
(-1/2)ln|1-y^2|+C=ln|x|
|x|=Cexp((-1/2)ln|1-y^2|)
|x|=C(|1-y^2|)^(-1/2)