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