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