Find the general solution of the given differential equation. dy/dx + y = e^6x

Solution:

The given differential equation is

dy/dx + y = e^6x

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

P = 1 and Q = e^6x

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^6x )+ C

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

So we get

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

y = e^6x/7 + c.e^-x

Therefore, the general solution is y = e^6x/7 + c.e^-x.

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Find the general solution of the given differential equation. dy/dx + y = e^6x

Summary:

The general solution of the given differential equation dy/dx + y = e^6x is e^6x/7 + c.e^-x.