Question

\[\frac{dy}{dx} = \left( e^x + 1 \right) y\]

Answer 1

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