(3x^2y^3e^x+y^3+y^2)DX+(x^2y^3e^x-xy)sy=0
(3x2y3ex+y3+y2)dx+(x2y3ex−xy)dy=0M(x,y)=3x2y3ex+y3+y2N(x,y)=x2y3ex−xy∂M∂y=9x2y2ex+3y2+2y∂N∂x=2xexy3−y∂M∂y≠∂N∂x∂M∂y−∂N∂xN−M=9x2y2ex+3y2+3y−2xexy3−2x2y3ex−xy−y3−y2(3x^2y^3e^x+y^3+y^2)dx+(x^2y^3e^x-xy)dy=0\\ M(x,y)=3x^2y^3e^x+y^3+y^2\\ N(x,y)=x^2y^3e^x-xy\\ \frac{\partial M}{\partial y}=9x^2y^2e^x+3y^2+2y\\ \frac{\partial N}{\partial x}=2xe^xy^3-y\\ \frac{\partial M}{\partial y}\neq \frac{\partial N}{\partial x}\\ \frac{\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}}{N-M}=\frac{9x^2y^2e^x+3y^2+3y-2xe^xy^3}{-2x^2y^3e^x-xy-y^3-y^2}\\(3x2y3ex+y3+y2)dx+(x2y3ex−xy)dy=0M(x,y)=3x2y3ex+y3+y2N(x,y)=x2y3ex−xy∂y∂M=9x2y2ex+3y2+2y∂x∂N=2xexy3−y∂y∂M=∂x∂NN−M∂y∂M−∂x∂N=−2x2y3ex−xy−y3−y29x2y2ex+3y2+3y−2xexy3
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