Question

1/xy2+y4 is an integral factor of the differential equation(x2y+y2)dx+(y3-z3)dy=0 true or false

Answer 1

Given equation,

$(x^2y+y^2)dx+(y^3-x^3)dy=0$

Here, $M=x^2y+y^2, N=y^3-x^3$

Hence Integrating factor $I.F.=\dfrac{1}{Mx+Ny}=\dfrac{1}{x^3y+xy^2+y^4-x^3y}$

$=\dfrac{1}{xy^2+y^4}$

Hence $\dfrac{1}{xy^2+y^4}$ is an integrating factor of given equation.