求微分方程x^2ydx=(1-y^2+x^2-x^2y^2)dy的通解,要具体过程~谢谢啦~

问题描述:

求微分方程x^2ydx=(1-y^2+x^2-x^2y^2)dy的通解,要具体过程~谢谢啦~

x^2ydx=(1+x^2)(1-y^2)dy
(1-y^2)/y*dy=x^2/(1+x^2)*dx
(1/y-y)dy=(1-1/(1+x^2))dx
ln|y|-y^2/2=x-arctanx+C