For each the differential equations given, find the general solution :
$\frac{d y}{d x} + 3 y = e^{- 2 x}$

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Solution

$\frac{d y}{d x} + 3 y = e^{- 2 x}$

$\frac{d y}{d x} + P y = Q$

$P = 3, Q = e^{- 2 x}$

$I . F . = e^{\int P d x}$

$= e^{\int 3 d x}$

$= e^{3 x}$

$y \times I . F = \int Q \times I . F d x + c$

$y \times e^{3 x} = \int (e^{- 2 x} \times e^{3 x}) d x + c$

$y e^{3 x} = \int e^{x} d x + c$

$y e^{3 x} = e^{x} + c$

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