Question

show that the differetial equation y(y^2+2x)+2x(y^2+x)dy/dx=0 is not exact, but that it has an integrating factor o of the form u=x^2y^k, for some integer k. hence or otherwise, find the general solutionof this diferential equation

Answer 1

\[(y ^{3}+2xy)dx + (2xy ^{2}+2x ^{2})dy\]
\[M_y=3y^2 + 2x\]
\[N_x= 2y^2 + 4x\]
\[M_y \neq N_x\]
therefore D.E. is not Exact.