xdx+ydy=a2(xdy-ydx)/x2+y2
xdx+ydy=a2(xdy−ydx)x2+y2)d(x2+y2)=a2(xdy−ydx)x21+y2x2d(x2+y2)=a2d(yx)1+(yx)2 Integrating Both the sides∫d(x2+y2)=∫a2d(yx)1+(yx)2⇒x2+y2=a2arctan(yx)+C⇒x2+y2−a2arctan(yx)=Cxdx+ydy=\dfrac{a^2(xdy-ydx)}{x^2+y^2)}\\[9pt] d(x^2+y^2)=\dfrac{a^2\frac{(xdy-ydx)}{x^2}}{1+\frac{y^2}{x^2}}\\[9pt] d(x^2+y^2)=\dfrac{a^2d(\frac{y}{x})}{1+(\frac{y}{x})^2}\\[9pt] \text{ Integrating Both the sides}\\[9pt] \int d(x^2+y^2)=\int \dfrac{a^2d(\frac{y}{x})}{1+(\frac{y}{x})^2}\\[9pt] \Rightarrow x^2+y^2=a^2arctan(\dfrac{y}{x})+C\\[9pt] \Rightarrow x^2+y^2-a^2arctan(\dfrac{y}{x})=Cxdx+ydy=x2+y2)a2(xdy−ydx)d(x2+y2)=1+x2y2a2x2(xdy−ydx)d(x2+y2)=1+(xy)2a2d(xy) Integrating Both the sides∫d(x2+y2)=∫1+(xy)2a2d(xy)⇒x2+y2=a2arctan(xy)+C⇒x2+y2−a2arctan(xy)=C
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