$$w-\ln\left|a\left(pH\right)^2+He^{ra}\right| = ln\left|\frac{y}{HN}\right|$$
$$w = \ln\left|\left(a\left(pH\right)^2+He^{ra}\right)\frac{y}{HN}\right|$$
$$e^w = \left(a\left(pH\right)^2+He^{ra}\right)\frac{y}{HN}$$
$$e^wN = \left(a\left(pH\right)^2+He^{ra}\right)\frac{y}{H}$$
$$e^wN = \left(ap^2H+e^{ra}\right)y$$
$$e^wN = ap^2Hy+e^{ra}y$$
$$ap^2Hy = e^wN-e^{ra}y$$
$$Happy = Ne^w-ye^{ar}$$