Answer to Question #168583 in Differential Equations for Wajahat

Question

(3x^2y^3e^x+y^3+y^2)DX+(x^2y^3e^x-xy)sy=0

Answer 1

$(3x^2y^3e^x+y^3+y^2)dx+(x^2y^3e^x-xy)dy=0\\ M(x,y)=3x^2y^3e^x+y^3+y^2\\ N(x,y)=x^2y^3e^x-xy\\ \frac{\partial M}{\partial y}=9x^2y^2e^x+3y^2+2y\\ \frac{\partial N}{\partial x}=2xe^xy^3-y\\ \frac{\partial M}{\partial y}\neq \frac{\partial N}{\partial x}\\ \frac{\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}}{N-M}=\frac{9x^2y^2e^x+3y^2+3y-2xe^xy^3}{-2x^2y^3e^x-xy-y^3-y^2}\\$