xdx+ydy=a2(xdy−ydx)x2+y2d(x2+y2)=a2(xdy−ydx)x21+y2x2d(x2+y2)=a2d(yx)1+y2x2∫d(x2+y2)=∫a2d(yx)1+(yx)2x2+y2=a2arctan(yx)+C∴x2+y2−a2arctan(yx)=C\displaystyle xdx+ydy = \frac{a^2(xdy-ydx)}{x^2+ y^2}\\ \mathrm{d}(x^2 +y^2) = \frac{a^2\frac{(xdy-ydx)}{x^2}}{1 + \frac{y^2}{x^2}}\\ \mathrm{d}(x^2 +y^2) = \frac{a^2\mathrm{d}\left(\frac{y}{x}\right)}{1 + \frac{y^2}{x^2}}\\ \int \mathrm{d}(x^2 +y^2) = \int \frac{a^2\mathrm{d}\left(\frac{y}{x}\right)}{1 + \left(\frac{y}{x}\right)^2}\\ x^2 +y^2 = a^2 \arctan\left(\frac{y}{x}\right) + C\\ \therefore x^2 +y^2 - a^2 \arctan\left(\frac{y}{x}\right) = C\\xdx+ydy=x2+y2a2(xdy−ydx)d(x2+y2)=1+x2y2a2x2(xdy−ydx)d(x2+y2)=1+x2y2a2d(xy)∫d(x2+y2)=∫1+(xy)2a2d(xy)x2+y2=a2arctan(xy)+C∴x2+y2−a2arctan(xy)=C
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Dear Shiv, please use the panel for submitting a new question. Please provide the full description of the question with all necessary requirements to avoid a confusion.
This is a nice method but can you please solve it by the procedure of exact differential equations. As in doing so I'm encountering a little problem.
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Dear Shiv, please use the panel for submitting a new question. Please provide the full description of the question with all necessary requirements to avoid a confusion.
Dear Shiv, please use the panel for submitting a new question. Please provide the full description of the question with all necessary requirements to avoid a confusion.
Dear Shiv, please use the panel for submitting a new question. Please provide the full description of the question with all necessary requirements to avoid a confusion.
This is a nice method but can you please solve it by the procedure of exact differential equations. As in doing so I'm encountering a little problem.