Find the general solution of differential equations $$\dfrac{ dy}{dx} + 2x = e^{3x}$$

Asked by Aaryan | 1 year ago |  120

##### Solution :-

From the question it is given that,

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

Transposing we get,

$$\dfrac{dy}{dx}$$ = e3x – 2x

Integrating on both side, we get,

∫dy = ∫(e3x – 2x) dx

We know that ∫xn dx = x(n + 1)/(n + 1)

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

y = ($$\dfrac{e^{3x}}{3}$$) – x2 + c

Therefore, y + x2 =$$\dfrac{1}{3}$$ (e3x) + c

Answered by Aaryan | 1 year ago

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