Find the general solution of the given differential equation. dy/dx + y = e^7x

Solution:

The given differential equation is

dy/dx + y = e^7x

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

P = 1 and Q = e^7x

Let us find the integrating factor(IF)

I= e^∫pdx = e^{∫1. dx} = e^x

Now multiply the differential equation with IF

y × IF = ∫Q× IF .dx + C

Substituting the values

e^x.y = e^x(e^7x) + C

e^x.(y) = e^8x /8 + C

So we get

y = e^8x /8 e^x + c. e^-x

y = e^7x/8 + c.e^-x

Therefore, the general solution is y = e^7x/8 + c.e^-x.

Find the general solution of the given differential equation. dy/dx + y = e^7x

Summary:

The general solution of the given differential equation dy/dx + y = e^7x is y = e^7x/8 + c.e^-x.