Hello
I stopped at this one:
$\displaystyle y(x^2-y^2+1)dx-x(x^2-y^2-1)dy=0$
I opened the brackets:
$\displaystyle yx^2dx - y^3dx + ydx-x^3dy+xy^2dy+xdy=0$
It will be:
$\displaystyle yx^2dx - y^3dx-x^3dy+xy^2dy+d(xy)=0$
then ?!!!!
Hello
I stopped at this one:
$\displaystyle y(x^2-y^2+1)dx-x(x^2-y^2-1)dy=0$
I opened the brackets:
$\displaystyle yx^2dx - y^3dx + ydx-x^3dy+xy^2dy+xdy=0$
It will be:
$\displaystyle yx^2dx - y^3dx-x^3dy+xy^2dy+d(xy)=0$
then ?!!!!
Re-writing gives
$\displaystyle -(x^2-y^2)(xdy-ydx) + xdy+ydx = 0$
$\displaystyle -(x^2-y^2)x^2 d\left(\dfrac{y}{x}\right) + d(xy) = 0$
$\displaystyle (1-\frac{x^2}{y^2}) x^2y^2d\left(\dfrac{y}{x}\right) + d(xy) = 0$
$\displaystyle \left(1-\dfrac{1}{\left(\frac{y}{x}\right)^2}\right) d\left(\dfrac{y}{x}\right) + \dfrac{d(xy)}{(xy)^2} = 0$