# 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 form of dy/dx +Py = Q

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

We first find the integrating factor(I)

I= e∫ᵖᵈˣ = e∫¹ᵈˣ = eˣ

Then we multiply the differential equation with I to get

I(dy/dx) + Iy = I( e^{2x })

⇒ eˣ (dy/dx) + eˣ (y) = eˣ (e^{2x} )

⇒ eˣ (y) = e³ˣ /3 +c

⇒ y = e³ˣ /3 eˣ +c

General solution , y = e²ˣ/3 +ce⁻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 = e²ˣ/3 +ce⁻ˣ.