The solution of the differential equation dy/dx + 4y = e^-10x is-

y= -e^-10x /6+ Ce^-4x 

The given differential equation is dy/dx + 4y = e^-10x

which is of the form dy/dx + py =Q   (Where p= 4 and Q=e^-10x )

Now, I.F. = e^∫pdx

I.F. = e^∫4dx 

So. I.F. = e^4x

The solution is given by:

y.(I.F.) = ∫Q x(I.F.)dx +C

⇒ y.e^4x =  ∫(e^-10x x e^4x) dx +C

so. y= -e^-10x /6+ Ce^-4x