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# Find the general solution of the given differential equation. dy/dx +2y = e^{3x}

**Solution:**

Given differential equation dy/dx +2y = e^{3x}

It is a linear differential equation in the form of dy/dx +Py = Q

Here, P=2 and Q= e^{3x}

We first find the integrating factor(IF)

IF= e^{∫p} ^{dx }= e^{∫2} ^{dx} =e^{2x }

Then we multiply the differential equation with IF to get

y× IF = ∫Q× IF dx + C

y e^{2x }= ∫e^{3x }.e^{2x} .dx + C

y e^{2x }= ∫e^{5x} .dx + C

⇒ e^{2x}(y) =e^{5x}/5 + C

⇒ y = e^{5x} /5e^{2x} + C /e^{2x}

y = e^{3x}/5 + Ce^{-}^{2x}

## Find the general solution of the given differential equation. dy/dx +2y = e^{3x}

**Summary:**

The general solution of the given differential equation. dy/dx +2y = e^{3x }is y = e^{3x}/5 + Ce^{-}^{2x}

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