Consider the differential equation

Question:

Consider the differential equation $\mathrm{y}^{2} \mathrm{dx}+\left(\mathrm{x}-\frac{1}{\mathrm{y}}\right) \mathrm{dy}=0$. It $\mathrm{y}(1)=1$, then $\mathrm{x}$ is given by :

  1. $1-\frac{1}{y}+\frac{\frac{1}{e^{y}}}{e}$

  2. $4-\frac{2}{y}-\frac{\frac{1}{e^{y}}}{e}$

  3. $3-\frac{1}{y}+\frac{\frac{1}{e^{y}}}{e}$

  4. $1+\frac{1}{y}-\frac{\frac{1}{e^{y}}}{e}$

Correct Option: , 4

Solution:

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