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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS3 Marks
Question
Solve the following differential equation:$\frac{dy}{dx} -\frac{y}{x} = 2x^{2}$
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Answer

Integrating factor $= e^{-\int\frac{dx}{x}}$$= e^{-\int\frac{- logx}{}} = \frac{1}{x} $
The solution of different equation is
$ y^\frac{1} {x} = {\int\frac{2x^{2}}{x}} dx + c$
$y^{{}{}} \frac{1}{x} = x^{2} + c$ or
$y = x^{3} + cx$

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