# 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 in the form of dy/dx +Py = Q

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

We first find the integrating factor(I)

I= e∫ᵖᵈˣ = e∫²ᵈˣ = e²ˣ

Then we multiply the differential equation with I to get

I(dy/dx) + Iy = I( e^{3x })

⇒ e²ˣ (dy/dx) + e²ˣ (y) = e²ˣ (e^{3x} )

⇒ e²ˣ (y) = e⁵ˣ /5 +c

⇒ y = e⁵ˣ /5e²ˣ +c

## 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 = e³ˣ/5e +c