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Consider the following differential equation

$$\left ( 1+y \right )\frac{dy}{dx}=y.$$

The solution of the equation that satisfies condition $y(1)=1$ is

  1. $2ye^{y}=e^{x}+e$
  2. $y^{2}e^{y}=e^{x}$
  3. $ye^{y}=e^{x}$
  4. $\left ( 1+y \right )e^{y}=2e^{x}$
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