求微分方程(x+8xy²)dx+(8x²y+3y)dy=0的通解
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![求微分方程(x+8xy²)dx+(8x²y+3y)dy=0的通解](/uploads/image/z/5409135-63-5.jpg?t=%E6%B1%82%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%28x%2B8xy%26%23178%3B%29dx%2B%288x%26%23178%3By%2B3y%29dy%3D0%E7%9A%84%E9%80%9A%E8%A7%A3)
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求微分方程(x+8xy²)dx+(8x²y+3y)dy=0的通解
求微分方程(x+8xy²)dx+(8x²y+3y)dy=0的通解
求微分方程(x+8xy²)dx+(8x²y+3y)dy=0的通解
xdx+3ydy+8xy^2dx+8x^2ydy=0
1/2d(x^2)+3/2d(y^2)+4d(x^2y^2)=0
两边积分:1/2x^2+3/2y^2+4x^2y^2=C
即x^2+3y^2+8x^2y^2=C