Solve the following differential equation: dy dx + 2y = 6 e^ x - Vidyadip

Question

Solve the following differential equation:

$\frac{dy}{dx} + 2y = \text6 {e^{x}}$

✓

Answer

$\text{I.F.} = e^{\int 2dx} = e^{2x}$

$\therefore \text{the solution is} $

$y . e^{2{x}} = 6 \int e^{3x} \text{dx + c} $

$y . e^{2x} ={\text{2 e}}^{3x}+ c$

or $y = \text{2 e}^{x} + {\text{c e}^{-2x}}$

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