求微分方程Y*dx+(x+y*y)dy=0
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求微分方程Y*dx+(x+y*y)dy=0
![求微分方程Y*dx+(x+y*y)dy=0](/uploads/image/z/7681659-51-9.jpg?t=%E6%B1%82%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8BY%EF%BC%8Adx%EF%BC%8B%EF%BC%88x%2By%2Ay%29dy%3D0)
∵ydx+(x+y²)dy=0
==>ydx+xdy+y²dy=0
==>d(xy)+1/3d(y³)=0
∴xy+y³/3=C/3 (C是积分常数)
故3xy+y³=C (C是积分常数)
==>ydx+xdy+y²dy=0
==>d(xy)+1/3d(y³)=0
∴xy+y³/3=C/3 (C是积分常数)
故3xy+y³=C (C是积分常数)