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Solving: (xy−x)dx+(xy+y)dy=0\left(\sqrt{xy}-\sqrt{x}\right)dx+\left(\sqrt{xy}+\sqrt{y}\right)dy=0
Solve instead: (xy−x)dx+(xy+y)dy\left(\sqrt{xy}-\sqrt{x}\right)dx+\left(\sqrt{xy}+\sqrt{y}\right)dy

Exercise

(xy−x)dx+(xy+y)dy\left(\sqrt{xy}-\sqrt{x}\right)dx+\left(\sqrt{xy}+\sqrt{y}\right)dy

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Final answer to the exercise

(y−1)2+4y−4+2ln⁡∣y−1∣=−(1+x)2+4x−2ln⁡∣1+x∣+C1\left(\sqrt{y}-1\right)^2+4\sqrt{y}-4+2\ln\left|\sqrt{y}-1\right|=-\left(1+\sqrt{x}\right)^2+4\sqrt{x}-2\ln\left|1+\sqrt{x}\right|+C_1

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