x^2ydx=(1-y^2+x^2-x^2y^2)dy的通解,求详细过程.
问题描述：
x^2ydx=(1-y^2+x^2-x^2y^2)dy的通解,求详细过程.
答
x^2ydx=(1-y^2+x^2-x^2y^2)dy=(1-y^2)(1+x^2)dy
所以
[x^2/(1+x^2)]dx=[(1-y^2)/y]dy
[1-1/(1+x^2)]dx=(1/y-y)dy
所以x-arctanx=lny-y^2/2+c