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Question

Solve:
(2x2+6xyy2)dx+(3x22xy+y2)dy=0

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Solution

Given integral equation (2x2+6xyy2)dx+(3x22xy+y2)dy=0
Group the given terms as follow,
2x2dx+y2dy(y2dx+2xydy)+3x2dy+6xydx=02x2dx+y2dyd(xy2)+3d(x2y)=0
Integrating, we get
2x2dx+y2dyd(xy2)+3d(x2y)=0
2x33+y33xy2+3x2y=C2x3+y33xy2+9x2y=C Where C=3C


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