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GATE Mechanical 2022 Set 2 | Question: 26

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For the exact differential equation,

$$\frac{du}{dx}= \frac{-xu^{2}}{2+x^{2}u},$$

which one of the following is the solution?

  1. $u^{2} + 2x^{2} =$ constant
  2. $xu^{2} + u =$ constant
  3. $\frac{1}{2}x^{2}u^{2} + 2u =$ constant
  4. $\frac{1}{2}ux^{2} + 2x =$ constant
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