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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS3 Marks
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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