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Question
\[\frac{dy}{dx} + 4x = e^x\]
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Solution
We have,
\[\frac{dy}{dx} + 4x = e^x \]
\[ \Rightarrow \frac{dy}{dx} = e^x - 4x\]
\[ \Rightarrow dy = \left( e^x - 4x \right)dx\]
Integrating both sides, we get
\[\int dy = \int\left( e^x - 4x \right)dx\]
\[ \Rightarrow y = e^x - 2 x^2 + C\]
\[ \Rightarrow y + 2 x^2 = e^x + C\]
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