show that the general solution of
dy/dx=exp(px-qy) , with p,q E Reals, can be written as y= aln(bexp(px)+w)
and express a, b and w in terms of p,q and an arbritrary constant C
I believe I have to integrate as differentiating y will not produce a constant so
let px-qy=v
dy/dx=(p-dv/dx)/q
dv/dx=p-qe^v=p(1-(q/p)e^v)
seperate variables
int(p/p-qe^v)dv=int(p)dx
v-ln(p-qe^v)+c=px
qy= c-ln(p-qexp(px-qy))
How to get in required form?