From the question it is given that,

\( \dfrac{dy}{dx} + 2x = e^{3x}\)

Transposing we get,

\( \dfrac{dy}{dx} \) = e^{3x} – 2x

Integrating on both side, we get,

∫dy = ∫(e^{3x} – 2x) dx

We know that ∫x^{n} dx = x^{(n + 1)}/(n + 1)

y = \( \dfrac{e^{3x}}{3} – \dfrac{2x^2}{2} + c\)

y = (\( \dfrac{e^{3x}}{3}\)) – x^{2} + c

Therefore, y + x^{2} =\( \dfrac{1}{3}\) (e^{3x}) + c

Find the particular solution satisfying the given condition \( (\dfrac{dy}{dx}) = (x – 1)\dfrac{dy}{dx} = 2x^3y\)

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