\exists U(x,y):U'_x=P,U'_y=Q\\ U=\int(2y-\dfrac{1}{x})dy=y^2-\dfrac{y}{x}+\phi(x)\\ =>\dfrac{y}{x^2}+\phi'(x)=\dfrac{y}{x^2}=>\phi'(x)=0=>\phi(x)=C_1=>U=y^2-\dfrac{y}{x}+C_1\\ y^2-\dfrac{y}{x}=C" alt="\dfrac{1}{x}dx+(2x-\dfrac{1}{y})dy=0\\ \dfrac{y}{x^2}dx+(2y-\dfrac{1}{x})dy=0\\ P= \dfrac{y}{x^2},Q=2y-\dfrac{1}{x},P'_y=Q'_x=\dfrac{1}{x^2}=>\exists U(x,y):U'_x=P,U'_y=Q\\ U=\int(2y-\dfrac{1}{x})dy=y^2-\dfrac{y}{x}+\phi(x)\\ =>\dfrac{y}{x^2}+\phi'(x)=\dfrac{y}{x^2}=>\phi'(x)=0=>\phi(x)=C_1=>U=y^2-\dfrac{y}{x}+C_1\\ y^2-\dfrac{y}{x}=C" align="absmiddle" class="latex-formula">