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