Divide throughout by x:

`(dy)/(dx)-4/xy=x^5e^x`

Here,

`P(x)=-4/x` and `Q(x)=x^5e^x`.

`"IF"=e^(intPdx)` `=e^(int-4/xdx)` `=e^(-4ln\ x)` `=e^(ln\ x^-4)` `=x^-4`

Now

`Qe^(intPdx)=(x^5e^x) x^-4=xe^x`

Applying the formula: `ye^(intPdx)=intQe^(intPdx)dx+K` gives

`y\ x^(-4)=intxe^xdx+K`

This requires integration by parts, with

`u=x,` and `dv=e^xdx`

This gives us

`du=dx,` and `v=e^x`.

So

`y\ x^-4=xe^x-e^x+K`

Multiplying throughout by x4 gives us `y` as an explicit function of `x`:

`y=x^5e^x-x^4e^x+Kx^4`