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Tag: differential equations

Solution to the differential equation \( \frac{dy}{dx} + 2y = e^{-x} \), \( y(0) = 1 \)

This is a first-order linear non-homogeneous differential equation. The general form is:

\[ \frac{dy}{dx} + P(x)y = Q(x) \]

Here, \( P(x) = 2 \) and \( Q(x) = e^{-x} \).

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