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

**Solution:**

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

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

Here, P=1 and Q= e^{2x}

We first find the integrating factor(IF)

I= e^{∫pdx} =e^{∫1. dx} = e^{x}

Then we multiply the differential equation with IF to get

y× IF = ∫Q× IF .dx + C

⇒ e^{x} y = e^{x}(e^{2x} )+ C

⇒ e^{x} (y) = e^{3x} /3 + C

⇒ y =e^{3x} /3 e^{x} +c. e^{-x}

General solution , y = e^{2x}/3 +c.e^{-x}

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

**Summary:**

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

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