\left(x\,e^{-2\,y}+\frac{1}{x}\,\tan\left(y\right)+2\,x\right)\,\mathrm{d}x+\left(\sec^{2}\left(y\right)\,\ln\left(y\right)-x^{2}\,e^{-2\,y}+1\right)\,\mathrm{d}y=0
You asked:
Investigate the equation: \(\left(x \cdot {e}^{-\left( 2 y \right)} + \frac{1}{x} \cdot \tan\left( y \right) + 2 x\right) \cdot d x + \left({\sec\left( y \right)}^{2} \cdot \ln\left( y \right) - {x}^{2} \cdot {e}^{-\left( 2 y \right)} + 1\right) \cdot d y = 0\).