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D Y D X + 4 X = E X - Mathematics

Sum

\[\frac{dy}{dx} + 4x = e^x\]

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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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APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 21 | Page 145
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