First order ODE involving substitution

Hey guys, I'm new here, rather stuck on this IVP. Full working would be lovely as I haven't come across substitution before and have attempted this problem about 7 times so far..

By making the substitution z = 3x - y, show that solving the initial value problem

y' = y -3x -5 -1/(3x -y +8), y(0) = 0,

leads to

(3x -y +8)^2 = 65e^2x -1.

Any help guys? I've tried this problem multiple times, probably doesn't help that I haven't been taught how substitutions come into ODE's.. Many thanks in advance :)

Re: First order ODE involving substitution

Using the substitution suggested will make the equation more manageable.

using gives

Re: First order ODE involving substitution

I see that, but my problem is I can't solve the equation from there, each time I try to solve it I get a different large mess of working that goes nowhere.

Re: First order ODE involving substitution