Solve the following differential equation dy dx =(e^x+1)y - Vidyadip

Question

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=(\text{e}^\text{x}+1)\text{y}$

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Answer

We have $\frac{\text{dy}}{\text{dx}}=(\text{e}^\text{x}+1)\text{y}$$\Rightarrow\frac{1}{\text{y}}\text{dy}=(\text{e}^\text{x}+1)\text{dx}$
Integrating both sides, we get
$\frac{1}{\text{y}}\text{dy}=(\text{e}^\text{x}+1)\text{dx}$
$\Rightarrow\log|\text{y}|=\text{e}^\text{x}+\text{x} +\text{C}$ Hence, $\Rightarrow\log|\text{y}|=\text{e}^\text{x}+\text{x} +\text{C}$ is the required solution.

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