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Question Number 93512 by Shakhzod last updated on 13/May/20

$$(xy+\sin y)dx+(0.5x^2+x\cos y)dy=o$$

Commented by i jagooll last updated on 14/May/20

$$\sin \mathrm{ydx}+\mathrm{xcos}\mathrm{ydy}=-0.{5\mathrm{x}}^2\mathrm{dy}-\mathrm{xydx}$$$$\mathrm{d}\left(\mathrm{xsin}\mathrm{y}\right)=-(\frac{1}{2}{\mathrm{x}}^2\mathrm{dy}+\mathrm{xydx})$$$$\mathrm{d}\left(\mathrm{xsin}\mathrm{y}\right)=-\mathrm{d}\left(\frac{1}{2}{\mathrm{x}}^2\mathrm{y}\right)$$$$\int \mathrm{d}\left(\mathrm{xsin}\mathrm{y}\right)=-\int \mathrm{d}\left(\frac{1}{2}{\mathrm{x}}^2\mathrm{y}\right)$$$$\mathrm{xsin}\mathrm{y}=-\frac{1}{2}{\mathrm{x}}^2\mathrm{y}+\mathrm{C}$$$$\frac{1}{2}\mathrm{x}(2\sin \mathrm{y}+\mathrm{xy})=\mathrm{C}$$

Commented by Shakhzod last updated on 13/May/20

$$GoooooD$$

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